Exhibit (a)(1)(iii)

FORM OF LETTER OF TRANSMITTAL AND REPURCHASE REQUEST FORM

Regarding Interests in

FRANKLIN LEXINGTON PRIVATE MARKETS FUND

Tendered Pursuant to the Offer to Purchase

Dated August 15, 2025

THIS LETTER OF TRANSMITTAL MUST BE

RECEIVED BY SS&C GIDS, Inc.

BY SEPTEMBER 15, 2025.

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE

AT 4:00 P.M., EASTERN TIME, ON SEPTEMBER 15, 2025,

UNLESS THE OFFER IS EXTENDED.

Complete This Letter Of Transmittal And Return To:

SS&C GIDS, Inc.

PO Box 219520

Kansas City, MO 64121-9520

Phone: (844) 534-4627

 

Letter of Transmittal Page 1 of 2

Ladies and Gentlemen:

The undersigned hereby tenders to Franklin Lexington Private Markets Fund, a closed-end, non-diversified management investment company organized as a Delaware statutory trust under the laws of the State of Delaware (the “Fund”), the beneficial interests in the Fund or portion thereof (the “Shares”) held by the undersigned, described and specified below, on the terms and conditions set out in the Offer to Purchase, dated August 15, 2025 (the “Offer”), receipt of which is hereby acknowledged, and in this Letter of Transmittal. THE OFFER AND THIS LETTER OF TRANSMITTAL ARE SUBJECT TO ALL THE TERMS AND CONDITIONS SET OUT IN THE OFFER, INCLUDING, BUT NOT LIMITED TO, THE ABSOLUTE RIGHT OF THE FUND TO REJECT ANY AND ALL TENDERS DETERMINED BY IT, IN ITS SOLE DISCRETION, NOT TO BE IN THE APPROPRIATE FORM.

The undersigned hereby sells to the Fund the Shares tendered pursuant to this Letter of Transmittal. The undersigned warrants that it has full authority to sell the Shares tendered hereby and that the Fund will acquire good title to the Shares, free and clear of all liens, charges, encumbrances, conditional sales agreements or other obligations relating to this sale, and not subject to any adverse claim, when and to the extent the Shares are repurchased by the Fund. Upon request, the undersigned will execute and deliver any additional documents necessary to complete the sale in accordance with the terms of the Offer.

The undersigned recognizes that under certain circumstances set out in the Offer, the Fund may not be required to repurchase the Shares tendered hereby. The undersigned further understands and agrees that if the undersigned tenders some but not all of its Shares for repurchase, the undersigned will be required to maintain a minimum account balance of $10,000. Such minimum ownership requirement may be waived by the Board, in its sole discretion. If such requirement is not waived by the Board, the Fund may redeem all of the undersigned’s Shares. To the extent the undersigned seeks to tender all of the Shares it owns and the Fund repurchases less than the full amount of Shares that the undersigned requests to have repurchased, the undersigned may maintain a balance of Shares of less than $10,000 following such Share repurchase.

The Fund will provide payment to the undersigned whose Shares have been accepted for repurchase an amount equal to at least 95% of the value of the repurchased Shares, based on the unaudited value of the Fund as of September 30, 2025, subject to an extension of the Offer as described in Section 8 of the Offer. The payment of the repurchase amount for the Shares tendered by the undersigned will be made by wire transfer of the funds to an account designated by the undersigned in this Letter of Transmittal. The Fund may hold back a portion of the amount due to the undersigned, which shall not exceed 5% of the total amount due to the undersigned. If there is such a holdback, the second and final payment for the balance due shall be paid no later than 5 business days after the completion of the annual audit of the Fund’s financial statements for the fiscal year in which the applicable repurchase is effected, with such balance being subject to adjustment as a result of the Fund’s annual audit or as a result of any other corrections to the Fund’s net asset value as of September 30, 2025.

All authority conferred or agreed to be conferred in this Letter of Transmittal will survive the death or incapacity of the undersigned and the obligation of the undersigned hereunder will be binding on the heirs, personal representatives, successors and assigns of the undersigned. Except as stated in Section 6 of the Offer, this tender is irrevocable.

PLEASE MAIL TO: SS&C GIDS, INC. ATTN: FRANKLIN LEXINGTON PRIVATE MARKETS FUND,

PO Box 219520, Kansas City, MO 64121-9520

FOR ADDITIONAL INFORMATION: PHONE: (844) 534-4627

 

Letter of Transmittal Page 2 of 2

Alternatives by FRANKLIN TEMPLETON Franklin Lexington Private Markets Fund Repurchase Request Form If completing by hand, please print clearly in CAPITAL LETTERS using blue or black ink. PARTS 1, 2, 3, 4 AND 5 MUST BE COMPLETED FOR TENDER REQUEST TO BE IN GOOD ORDER FOR PROCESSING PLEASE MAIL TO: Regular Mail: Franklin Templeton P.O. Box 219520 Kansas City, MO 64121-9520 Overnight: Franklin Templeton 801 Pennsylvania Ave, Suite 219520, Kansas City, MO 64105-1307 Email: LEGGMASON.AI@sscinc.com Fax: (833) 411-5611 FOR ADDITIONAL INFORMATION: PHONE: (844) 534-4627 PLEASE CONTACT YOUR FINANCIAL INTERMEDIARY BEFORE SUBMITTING YOUR TENDER REQUEST. 1 NAME AND ADDRESS Beneficial Owner(s) Information Franklin Lexington Private Markets Fund Account Number Full Account Registration Line 1 Full Account Registration Line 2 Address Telephone Number Financial Professional Firm Name Financial Professional Rep Name Financial Professional Telephone Number FOR CUSTODIAL ACCOUNTS ONLY1 Custodial Account Number Custodian Name Custodian Address Custodian City, State, Zip Custodian Telephone Number 1. If your Custodian is First Trust Retirement, please also complete the First Trust Retirement IRA Withdrawal/RMD Form at https://secure.alpsinc.com/MarketingAPI/api/v1/Content/firsttrustretirement/firsttrustretirement-403df-franklintempleton-20240813.pdf. (continued) page 1 of 4

1 NAME AND ADDRESS (Contd.) Registered Holder Information (if different than above; print name exactly as it appears on the subscription agreement or as indicated on the stock ledger maintained by the Funds transfer agent)* * For positions registered in the name of a custodian, the signature of the custodian is required. Please ensure the custodian signs this Repurchase Request Form in the Registered Holder Signature block in Part 5. Name of Registered Holder Address Tax ID No. Telephone Number 2 AMOUNT OF SHARES IN THE FUND BEING TENDERED Class S Class D Class I Class M Entire amount of Shares Portion of Class S Shares $ or Number of Shares Portion of Class D Shares $ or Number of Shares Portion of Class I Shares $ or Number of Shares Portion of Class M Shares $ or Number of Shares The undersigned understands and agrees that if the undersigned tenders some but not all of its Shares for repurchase, the undersigned will be required to maintain a minimum account balance of $10,000. Such minimum ownership requirement may be waived by the Board of Trustees (the Board), in its sole discretion. If such requirement is not waived by the Board, the Fund may redeem all of the undersigneds Shares. To the extent the undersigned seeks to tender all of the Shares it owns and the Fund repurchases less than the full amount of Shares that the undersigned requests to have repurchased, the undersigned may maintain a balance of Shares of less than $10,000 following such Share repurchase. 3 COST BASIS INFORMATION (information required for tax reporting purposes) Per the Internal Revenue Service (IRS) regulation Basis Reporting by Securities Brokers and Basis Determination for Stock, the Fund is required to know the cost accounting method the owner(s) would like the Fund to use in calculating the gain or loss associated with this repurchase offer. If the owner(s) does not provide this information, the Fund will use its chosen default method, First-In, First-Out (FIFO). Note that the Funds default method may not be the most tax advantageous method. The owner(s) may want to consult their financial advisor or tax professional before completing this section. Select one option then complete the additional information requested, if applicable: First-In, First-Out (FIFO) First-In, First-Out uses the first lots purchased into the account to determine the cost basis of the Shares and to calculate the gain or loss. Specific Share Identification Specific Share Identification allows the owner(s) to select the Shares from any purchase or reinvested lot that has not previously been sold. Indicate in the table below the number and class of Shares and date of purchase for each lot to be repurchased in this transaction. To the extent all Shares tendered are not accepted by the Fund, the Fund will use the Shares listed in the first row of the table and proceed to the next row(s) as necessary until all Shares accepted by the Fund are accounted. Number of Shares Class of Shares Date of Purchase Note that a 2.00% early repurchase fee will be charged by the Fund with respect to any repurchase of Shares from a shareholder at any time prior to the day immediately preceding the one-year anniversary of the shareholders purchase of the Shares. In addition, if no withholding election is indicated below, IRS regulations require that 10% Federal income tax withholding be taken from your IRA distributions. We encourage you to consult your accountant or tax advisor regarding your IRA distributions. Even if you elect not to have Federal income tax withheld, you are liable for payment of Federal income tax on the taxable portion of your distribution. You may be subject to tax penalties under the estimated tax payment rules if your payments of estimated tax and withholdings are not adequate. Federal Income Tax Withholding is to be withheld at % (If a percentage is not specified, 10% will automatically be withheld). I elect NOT to have Federal Income Tax withheld. page 2 of 4 (continued)

4 NON-CUSTODIAL PAYMENT PAYMENT GUIDELINES: Proceeds for custodial accounts will automatically be issued to the Financial Intermediary (defined below) of record. Custodial signature required. If your Shares are held through a financial intermediary, such as a financial adviser, Custodian, Broker/Dealer, or other nominee (each, a Financial Intermediary), please ask your Financial Intermediary to submit the Repurchase Request Form on your behalf. Your Financial Intermediary may require alternate payment and/or delivery instructions, notwithstanding your request herein. Please contact your Financial Intermediary before submitting your tender request. If you invest in the Fund through a Financial Intermediary, please allow for additional processing time. Please deliver all proceeds via: Mail to the Financial Intermediarys address of record ACH to the Financial Intermediarys account of record Mail to the following address: Name Address ACH Federal Wire to the following account: Bank Name ABA Routing Number For Credit to: Name(s) on Bank Account Bank Account Number For Further Credit to: Name(s) on Investors Account Investor Account Number at Broker 5 SIGNATURE(S) The undersigned subscriber acknowledges that this request is subject to all the terms and conditions set forth in the Funds Prospectus, as amended and/or supplemented from time to time (the Prospectus) and the Offer to Purchase and all capitalized terms used herein have the meaning as defined in the Prospectus. This request is irrevocable except as described in the Offer to Purchase. The undersigned represents that the undersigned is the beneficial owner of the shares in the Fund to which this repurchase request relates, or that the person signing this request is an authorized representative of the tendering stockholder. In the case of joint accounts, each joint holder must sign this repurchase request. Requests on behalf of a foundation, partnership or any other entity should be accompanied by evidence of the authority of the person(s) signing. If Shares are registered in the name of a Financial Intermediary, such Financial Intermediary must execute this Repurchase Request Form, and the beneficial owner of the Shares hereby authorizes and directs the Financial Intermediary to execute this Repurchase Request Form. Beneficial Owner and Custodian Signature: Signature Print Name of Authorized Signatory (and Title if applicable) Date X Signature Print Name of Authorized Signatory (and Title if applicable) Date X Signature Print Name of Authorized Signatory (and Title if applicable) Date X Signature of Authorized Custodian, if applicable Print Name of Authorized Signatory (and Title if applicable) Date X Registered Holder Signature (if different than above; print name exactly as it appears on the subscription agreement or as indicated on the stock ledger maintained by the Funds transfer agent): X Signature Registered Holder Print Name of Registered Holder Title of Signatory Date (continued) page 3 of 4

THIS DOCUMENT REQUIRES A MEDALLION SIGNATURE GUARANTEE BELOW ONLY WHEN AUTHORIZED SIGNER(S) INSTRUCT THE FUND TO SEND TENDER PROCEEDS TO AN ADDRESS OR ACCOUNT OTHER THAN THE BROKER/CUSTODIAN ADDRESS OR ACCOUNT OF RECORD. MEDALLION SIGNATURE GUARANTEE STAMP IF YOUR SHARES ARE HELD THROUGH A FINANCIAL INTERMEDIARY, PLEASE ASK YOUR FINANCIAL INTERMEDIARY TO SUBMIT THE LETTER OF TRANSMITTAL ON YOUR BEHALF. PLEASE CONTACT YOUR FINANCIAL INTERMEDIARY BEFORE SUBMITTING YOUR TENDER REQUEST. page 4 of 4 US-GSS-6420008-6320008 FLEX-TRFRM 07/25 2025 Franklin Templeton. All rights reserved.