Exhibit 10.13

FIRST Amendment

to

BCA Note AND NOTE PURCHASE AGREEMENT

This First Amendment to BCA Note and Note Purchase Agreement (this “Amendment”), effective as of July 1, 2026, is by and between Mkango Rare Earths Limited (formerly Lancaster Exploration Limited), a British Virgin Islands company (the “Company”), and First Mile Pref Fund II LLC, a Delaware limited liability company (the “Investor”).

Recitals

Whereas, the Company executed and delivered to the Investor that certain BCA Note, dated July 2, 2025 (as the same has been and may from time to time further be amended, modified, supplemented or restated, the “BCA Note”) pursuant to that certain Note Purchase Agreement, dated as of June 2, 2025 (the “Note Purchase Agreement”), a copy of which is attached hereto as Exhibit A; and

Whereas, the parties have agreed to amend the BCA Note and Note Purchase Agreement as more fully set forth below.

Agreement

Now, Therefore, in consideration of the foregoing recitals and other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, and intending to be legally bound, the parties hereto agree as follows:

1. Definitions; Incorporation of Recitals. The recitals set forth above are hereby incorporated by reference into, and made a part of, this Amendment as if fully set forth herein. Capitalized terms used but not defined in this Amendment shall have the meanings given to them in the BCA Note, the Note Purchase Agreement, as applicable, or in the “BCA” (as such term is defined in BCA Note, as modified hereby).

2. Amendments to the BCA Note.

2.1 The Company name on the face of the BCA Note is amended in its entirety and replaced with “MKANGO RARE EARTHS LIMITED (formerly Lancaster Exploration Limited).”

2.2 The dollar amount on the face of the BCA Note is amended in its entirety and replaced with “$623,765.63 to reflect the current principal balance as of July 1, 2026.”

2.3 The first sentence of the preamble of the BCA Note is amended in its entirety and replaced with the following:

FOR VALUE RECEIVED, Mkango Rare Earths Limited (formerly Lancaster Exploration Limited), a British Virgin Islands company (the “Company”) promises to pay to the order of First Mile Pref Fund II LLC, a Delaware limited liability company (“Investor”), or Investor’s registered assigns, the principal sum of $623,765.63 (as adjusted pursuant to the terms herein, the “Principal Amount”), together with interest (as calculated below) from the date of this Convertible Promissory Note (as the same has been and may from time to time further be amended, modified, supplemented or restated, this “Note”) on the unpaid principal balance accruing at the Interest Rate (as defined below) pursuant to that certain Note Purchase Agreement by and between the Company and the investors listed therein, including Investor, dated June 2, 2025 (as the same may be amended or restated from time to time, the “Note Purchase Agreement”).

2.4 Section 1(a) of the BCA Note is amended in its entirety and replaced with the following:

“Maturity. If this Note is outstanding at December 31, 2026 (the “Maturity Date”), a dollar amount equal to $650,000 minus any principal payments made as of the Maturity Date plus any unpaid and accrued interest owing pursuant to Section 1(b), plus any other amounts due and owing under this Note and the Note Purchase Agreement with respect to the Note, shall be due and payable five days after receipt by the Company from Investor of a written demand for payment which demand shall not be made prior to the Maturity Date (but such demand may be made on the Maturity Date or at any time thereafter).”

2.5 Section 1(b) of the BCA Note is amended in its entirety and replaced with the following:

“Interest (a) . Accrued interest on this Note shall be payable in arrears on each of the Semiannual Date, the Annual Date and the Maturity Date. Subject to the receipt of approval from the TSX Venture Exchange and satisfaction of customary closing conditions (“TSX-V Conditional Approval”), nine percent (9%) per annum (the “In-kind Interest Rate”) of the Interest Rate shall be paid in kind and compound semiannually (the “In-kind Interest”), and three percent (3%) per annum (the “Cash Interest Rate”) of the Interest Rate shall be paid in cash (the “Cash Interest” and, together with the In-kind Interest, “Interest”). For the avoidance of doubt, (i) the semiannual compounding of the In-kind Interest on the Semiannual Date and the Annual Date shall be effected by the addition of a dollar amount equal to the In-Kind Interest payable at that time to the then outstanding principal amount of the BCA Note; and (ii) in the event TSX-V Conditional Approval is not obtained with respect to payment of the In-kind Interest by the date such payment is due, such interest shall be paid in cash. Further, the In-kind Interest shall accrue at the In-kind Interest Rate (x) on a principal amount of $500,000 (the “Original Principal Amount”) from the date hereof until the Annual Date (assuming semiannual compounding at the Semiannual Date); and (y) on the Principal Amount, which, for the avoidance of doubt, equals the Original Principal Amount plus all compounded In-kind Interest through the Annual Date plus $77,753.13, from the Annual Date until the Maturity Date (or the date this Note is released pursuant to Section 4(b) below, if earlier); and the Cash Interest shall accrue at the Cash Interest Rate on the Original Principal Amount for each period from the date hereof until the Semiannual Date, from the Semiannual Date to the Annual Date, and from the Annual Date to the Maturity Date (or the date this Note is released pursuant to Section 4(b) below, if earlier), with such Cash Interest accrued at the end of each period being paid at each of the Semiannual Date, the Annual Date, and the Maturity Date (or the date this Note is released pursuant to Section 4(b) below, if earlier), respectively.”

2.6 The words “were converted to Conversion Shares at the Conversion Price” in Section 1(f) of the BCA Note is replaced with the following: “were released in consideration for the issuance of Consideration Shares at the Consideration Price”.

2.7 Section 2 of the BCA Note is amended by adding a new Section 2(b) and (c), below, with existing Section 2(b) through (l) being renumbered as Sections 2(d) through (n), respectively:

“(b) “Annual Date” means July 1, 2026.

(c) “BCA” means that certain business combination agreement by and among the Company, CPTK, and the other parties thereto, as the same may be amended, restated, supplemented or otherwise modified from time to time.”

2.8 Section 2(f) (as updated in accordance with Section 2.7 above), is amended in its entirety and replaced with the following:

““Consideration Price” means $5.00 per Consideration Share.”

2.9 Section 2(g) (as updated in accordance with Section 2.7 above), is amended in its entirety and replaced with the following:

““Consideration Shares” means Class A Shares of the Company issued pursuant to the release of this Note in consideration for the issuance by the Company of Class A Shares.”

2.10 Section 2(n) (as updated in accordance with Section 2.7 above), is amended in its entirety and replaced with the following:

““Share Reclassification Board Approval” means the approval by the board of directors of the Company, subject to any required shareholder approval, of the amendment and restatement of its memorandum and articles of association to implement a variation of rights and a redesignation and reclassification of the Capital Shares.”

2.11 Section 3(a) of the BCA Note is amended in its entirety and replaced with the following:

“(a)      Failure to Pay. The Company fails to pay when due any principal, interest, fees, expenses, indemnities, enforcement costs, attorneys’ fees or any other amounts owing under this Note or the Note Purchase Agreement with respect to the Note, and such failure continues for five (5) days after the date such amount is due and payable;”

2.12 The final sentence of Section 3 of the BCA Note is amended in its entirety and replaced with the following:

“In addition to the right of repayment, upon the occurrence and during the continuance of any Event of Default, Investor may exercise any other right, power or remedy granted to it or permitted to it by law, either by suit in equity or by action at law, or both, and the Company shall reimburse Investor on demand for all out-of-pocket fees, costs and expenses, including but not limited to, reasonable attorneys’ fees and expenses, incurred by Investor in connection with the enforcement, collection, preservation or protection of Investor’s rights and remedies under this Note, the Note Purchase Agreement or any other Transaction Document.”

2.13 Section 4 of the BCA Note is amended in its entirety and replaced with the following:

“4. Debt-for-Equity Swap.

(a) Consideration; Cashout.

(i) If a Share Reclassification Board Approval occurs prior to the Maturity Date, and the Minimum Cash Condition (as defined in the BCA) is not satisfied at such time, then this Note shall be released in consideration for the issuance by the Company of such number of Consideration Shares equal to the sum of the Principal Amount and all accrued and unpaid Interest divided by the Consideration Price.

(ii) If a Share Reclassification Board Approval occurs and the Minimum Cash Condition (as defined in the BCA) is satisfied at such time, Investor may, in its discretion, either (A) release the debt in this Note in full pursuant to Section 4(a)(i), or (B) release the debt in this Note such that Investor is (1) paid the Cashout Amount, (2) issued a number of Consideration Shares equal to the Cashout Amount divided by $20.00, and (3) issued additional Consideration Shares, if any, equal to (x) the sum of the Principal Amount and all accrued and unpaid Interest minus the Cashout Amount divided by (y) the Consideration Price.

(iii) The Consideration Shares will not be subject to any lock-up or other restrictions set forth in the BCA, with exceptions of limitations required by applicable securities laws.

(iv) Notwithstanding the foregoing, in no event shall Investor be issued a number of Consideration Shares pursuant to this Note that would result in Investor’s ownership of Capital Shares exceeding 19.99% of the total issued and outstanding Capital Shares as of the date hereof (the “Capital Shares Cap”); provided that, to the extent that the number of Consideration Shares otherwise issuable to Investor pursuant to this Note would exceed the Capital Shares Cap, the Company shall pay to Investor, in cash, an amount equal to the Consideration Price multiplied by the Consideration Shares that Investor would have received but for the Capital Shares Cap.

(b) Administration. Upon the issuance of all Consideration Shares, if applicable, and payment in full of all cash amounts, if any, required to be paid to Investor pursuant to Section 4(a) (the “Debt-for-Equity Swap Realization”), the Company shall be forever released from its payment obligations and liabilities under this Note solely to the extent actually satisfied by such issuance and payment. For the avoidance of doubt, no release, cancellation, surrender or deemed satisfaction of this Note shall occur unless and until Investor has received indefeasible payment of all cash amounts then due and evidence reasonably satisfactory to Investor that all Consideration Shares have been validly issued, fully paid, non-assessable, freely transferable, and not subject to any lien, adverse claim, lock-up, contractual restriction, legend or other transfer restriction other than restrictions arising under applicable securities and/or tax laws. In connection with the Debt-for-Equity Swap Realization, Investor and the Company will execute and deliver to each other customary share purchase and related financing agreements, as applicable; provided that Investor shall not be required to execute any agreement or document that would impose any indemnity, release, lock-up, standstill, voting restriction, transfer restriction, waiver, covenant or other obligation on Investor not expressly set forth in this Note or otherwise reasonably acceptable to Investor, except as required under applicable securities and/or tax laws. Investor also agrees to deliver the original of this Note (or a notice to the effect that the original Note has been lost, stolen or destroyed and an agreement acceptable to the Company and Investor whereby the holder agrees to indemnify the Company from any actual loss incurred by it solely as a result of an unauthorized third-party claim in connection with the loss of this Note) upon consummation of the Debt-for-Equity Swap Realization for cancellation; provided that this Note shall not be deemed released, cancelled or of no further force and effect until the Debt-for-Equity Swap Realization has been fully consummated as provided above (at which point this Note shall be deemed released). Any Debt-for-Equity Swap Realization shall be deemed to have been made immediately upon the actual issuance of the Consideration Shares and payment in full of all cash amounts, if any, required to be paid to Investor pursuant to Section 4(a), and on and after such date Investor shall be treated for all purposes as the record and beneficial holder of the Consideration Shares. As promptly as practicable, and in any event within two (2) business days, after the Debt-for-Equity Swap Realization, the Company or its successor (at its expense) will issue and deliver to Investor (or its nominee) a certificate or certificates evidencing the Consideration Shares (if certificated), or if the Consideration Shares are not certificated, will deliver evidence reasonably satisfactory to Investor (or its nominee) of the issuance of the Consideration Shares in book entry or other electronic format.”

2.14 Section 5 of the BCA Note is amended in its entirety and replaced with the following:

“5. Reference Date. The Company will have the right to set a reference date for the release of the accrued interest under this Note upon two (2) business days’ prior written notice to Investor, in consideration for the issuance by the Company of such number of Consideration Shares and payment of any Cashout Amount, if applicable, pursuant to Section 4(a) above (which reference date shall be no sooner than two (2) days prior to the applicable date of the Share Reclassification Board Approval, Event of Default, Dissolution Event, or Maturity Date), such that interest accrued through such reference date will be released and interest shall cease accruing after such reference date; provided that if such event does not occur when anticipated, such reference date will be retroactively adjusted to the date that is two (2) days prior to the date the Debt-for-Equity Swap Realization actually occurred.”

2.15 Section 6(g) of the BCA Note is amended in its entirety and replaced with the following:

“(g) Governing Law; Jurisdiction. This Note and all actions arising out of or in connection with this Note shall be governed by and construed in accordance with the laws of the State of New York, without regard to the conflicts of law provisions of the State of New York, or of any other state. Each party irrevocably and unconditionally submits, for itself and its property, to the exclusive jurisdiction of the state and federal courts located in the State of New York, County of New York, and any appellate court from any thereof, in any action, claim, controversy or proceeding arising out of or relating to this Note, the transactions contemplated hereby or the enforcement hereof. Each party irrevocably and unconditionally waives any objection that it may now or hereafter have to the laying of venue of any such action, claim, controversy or proceeding in any such court, and irrevocably waives any claim that any such action, claim, controversy or proceeding has been brought in an inconvenient forum. Each party agrees that a final judgment in any such action, claim, controversy or proceeding shall be conclusive and may be enforced in any other jurisdiction by suit on the judgment or in any other manner provided by law. Each party irrevocably consents to service of process in the manner provided for notices under the Note Purchase Agreement and agrees that nothing herein shall affect the right of Investor to serve process in any other manner permitted by applicable law or to bring any action or proceeding against the Company or its assets in any other jurisdiction for purposes of enforcement of any judgment or equitable relief.”

2.16 Section 6(i) shall be retained but shall also include the following sentences:

“Notwithstanding anything to the contrary in Section 1(e) of the Note Purchase Agreement, any payment of In-kind Interest (including such imputed interest) or Cash Interest to be made under this Note shall be made free and clear of all deductions or withholdings; provided that such payment shall be subject to a deduction or withholding for United Kingdom withholding tax or any deduction or withholding for or on account of United Kingdom income tax, in each case at the applicable rate, in respect of any payment or deemed payment (including any issuance of Consideration Shares in respect of interest) under this Note (“UK WHT”), as reasonably estimated by the Company to be due, without regard to whether UK WHT is, or becomes, in fact due, including in a situation where the Company has received a gross payment direction from HMRC in relation to the payment of the In-kind Interest and/or the Cash Interest. For the avoidance of doubt, in the Company’s reasonable discretion, such withheld dollar amount may be applied solely to the payment of In-kind Interest by reducing the number of Consideration Shares otherwise issuable to the Investor by Consideration Shares having a value (at the Consideration Price) equal to that withheld amount.”

2.17 Section 6 of the BCA Note is amended by adding a new Section 6(k) as follows:

“(k) Tax Cooperation. The Investor shall, at the Company’s reasonable written request, use commercially reasonable efforts to cooperate with the Company (and with any paying agent or professional adviser acting for the Company at the Company’s expense) in obtaining, maintaining and giving effect to any exemption from, or reduction in the rate of, any deduction or withholding for or on account of Tax that is or would otherwise be required by law in respect of any payment or deemed payment made or to be made under this Note, including any relief, exemption or reduced rate available under an applicable double taxation treaty (including the Convention between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the United States of America for the Avoidance of Double Taxation, as amended, the “US/UK Treaty”). Without limiting the foregoing, the Investor shall:

(i) promptly complete, sign and deliver to the Company (or, as directed by the Company, to HM Revenue & Customs (“HMRC”) or other relevant taxing authority) any forms, certifications, documentation or information reasonably requested by the Company that is required by the HMRC to establish or preserve such exemption, reduction or relief, including a certificate of tax residence from the U.S. Internal Revenue Service and information reasonably necessary to establish the Investor’s beneficial entitlement to the relevant payments and its eligibility under any limitation-on-benefits or similar provision of the US/UK Treaty;

(ii) reasonably cooperate in the preparation, submission and prosecution of any application, claim or filing (including any application for a direction to pay gross or at a reduced rate, and any use of the HMRC double taxation treaty passport scheme) required to obtain or maintain such exemption, reduction or relief;

(iii) promptly notify the Company in writing if it becomes aware of any change in its circumstances (including its tax residence or beneficial ownership) that would or might affect the availability or continuation of any such exemption, reduction or relief, or the accuracy of any certification or information previously provided; and

(iv) use commercially reasonable efforts to maintain its eligibility for any such exemption, reduction or relief for so long as any amount is or may become payable under this Note.

Notwithstanding anything to the contrary in this Section 6(k), Investor shall not be required to (i) take any action, omit to take any action, or refrain from taking any action, or (ii) provide any information, certification or documentation, in each case if Investor reasonably determines that doing so could adversely affect Investor’s tax, legal, regulatory or economic position or impose any material burden on Investor.”

2.18 Section 6 of the BCA Note is amended by adding a new Section 6(l) as follows:

“(l) UK Withholding Tax Indemnity.

(i) If, following the process contemplated by 6(k), Investor actually receives a cash repayment, cash refund or cash credit from HMRC or another applicable taxing authority in respect of UK WHT previously deducted or withheld by the Company and remitted to such taxing authority, then Investor shall, within ten (10) business days after actual receipt thereof, pay to the Company an amount equal to such cash repayment, refund or credit actually received by Investor, net of any reasonable out-of-pocket costs, expenses, Taxes or other amounts incurred or payable by Investor in obtaining, receiving or retaining such repayment, refund or credit; provided that Investor has provided to the Company reasonably detailed supporting calculations and documentation from Investor with respect to such amounts withheld from Investor’s payment; and provided further that Investor shall not be required to make any payment to the Company unless and until Investor has actually received the applicable cash benefit and such benefit is final, non-appealable and not subject to clawback, adjustment, recapture or repayment.

(ii) If the monetary amount of any cash repayment, cash refund, cash credit or other cash tax benefit actually received and retained by Investor pursuant to Section 6(l)(i) is less than the monetary amount of the UK WHT actually deducted or withheld by the Company and remitted to the applicable taxing authority, or if no such cash repayment, cash refund, cash credit or other cash tax benefit is actually received by Investor following Investor’s commercially reasonable cooperation pursuant to Section 6(k) (such unrecovered amount, the “Residual UK WHT”), then Investor shall pay to the Company in cash an amount equal to fifty percent (50%) of the Residual UK WHT; provided that (A) Investor shall have no obligation to make any such payment unless the Company has actually remitted the applicable UK WHT to the relevant taxing authority and provided Investor with reasonable evidence of such remittance, (B) the Residual UK WHT shall be calculated net of any reasonable out-of-pocket costs, expenses, Taxes or other amounts incurred or payable by Investor in seeking, obtaining, receiving or retaining any such repayment, refund, credit or other tax benefit, provided that Investor has provided to the Company reasonably detailed supporting calculations and documentation from Investor with respect to such amounts withheld from Investor’s payment, (C) Investor shall not be liable for any penalties, interest, additions to tax or similar amounts arising from the Company’s failure to deduct, withhold, remit, report or otherwise comply with applicable law, to the extent such failure was not attributable to Investor’s negligence or failure to, or exercise of any discretion not to, fulfill its obligations under Section 6(k) after giving effect to the limitations and carveouts set forth in the last paragraph of Section 6(k), and (D) any payment required under this Section 6(l)(ii) shall be due within ten (10) business days after the final determination of the Residual UK WHT and Investor’s receipt of reasonably detailed supporting calculations and documentation from the Company.

(iii) This Section 6(l) is without prejudice to Section 6(i), and does not itself create any obligation of the Company to gross up or pay any additional amount to the Investor unless otherwise expressly required under this Note or the Note Purchase Agreement.”

2.19 Section 6 of the BCA Note is amended by adding a new Section 6(m) as follows:

“(m) Conflicts. Notwithstanding anything to the contrary contained in the Note Purchase Agreement, in the event of any conflict, inconsistency or discrepancy between the terms of this Note and the terms of the Note Purchase Agreement, the terms of this Note shall govern and control.”

3. Limitation of Amendments. The amendments set forth in Section 2 above are effective solely for the purposes set forth herein and shall be limited precisely as written and shall not be deemed to (a) be a consent to any amendment, waiver or modification of any other term or condition of the BCA Note or any other Transaction Document, or (b) otherwise prejudice any right or remedy which the Investor may now have or may have in the future under or in connection with the BCA Note or the other Transaction Documents.

4. Integration. The Note Purchase Agreement, this Amendment and the BCA Note represent the entire agreement about this subject matter and supersede prior negotiations or agreements. All prior agreements, understandings, representations, warranties, and negotiations between the parties about the subject matter of this Amendment and the BCA Note merge into this Amendment and the BCA Note.

5. Representations; Further Assurances. The Company represents and warrants to Investor that (a) this Amendment has been duly authorized, executed and delivered by the Company and constitutes a legal, valid and binding obligation of the Company enforceable against the Company in accordance with its terms, (b) the execution, delivery and performance of this Amendment do not violate the Company’s organizational documents, any applicable law or any material agreement binding on the Company, and (c) the representations in Section 2(e) of the Note Purchase Agreement remain accurate in all material respects. The Company shall execute and deliver such further instruments and take such further actions as Investor may reasonably request to carry out the intent of this Amendment and protect Investor’s rights hereunder.

6. Counterparts; Electronic Signatures. This Amendment may be executed in any number of counterparts and all of such counterparts taken together shall be deemed to constitute one and the same instrument. Each party hereto may execute this Amendment by electronic means and recognizes and accepts the use of electronic signatures and records by any other party hereto in connection with the execution and storage hereof.

[Signature page follows]

In Witness Whereof, the parties hereto have caused this Amendment to be duly executed and delivered as of the date first written above.

[First Amendment to BCA Note and Note Purchase Agreement]

EXHIBIT A

BCA NOTE AND NOTE PURCHASE AGREEMENT

[attached hereto]

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