Exhibit 5.1

Lucas GC Limited

Palm Grove Unit 4

265 Smith Road, George Town

P.O. Box 52A Edgewater Way, #1653

Grand Cayman KY1-9006

Cayman Islands

Attention: The Board of Directors

(Addressee)

Email dbulley@applebyglobal.com

Tel+852 2523 8123

Appleby Ref 473424.0001

28 October 2026

Suites 3504B-06

35/F, Two Taikoo Place

979 King’s Road

Quarry Bay

Hong Kong

Tel +852 2523 8123

applebyglobal.com

Managing Partner

David Bulley

Partners

Fiona Chan

Kitty Chan

Vincent Chan

Chris Cheng

Richard Grasby

Judy Lee

Michael Makridakis

John McCarroll SC

Lorinda Peasland

Eliot Simpson

Freya Xu

Dear Company

Lucas GC Limited (Company)

INTRODUCTION

We act as Cayman Islands legal adviser to the Company, and this legal opinion as to Cayman Islands law is addressed to you in connection with the Company’s filing of a registration statement on Form S-8, including all amendments or supplements thereto (Registration Statement, which term does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto) with the U.S. Securities and Exchange Commission (Commission) relating to the offering by the Company of an aggregate of 497,640 ordinary shares of a par value of US$0.00001 each (Offering Shares) issuable pursuant to the second amended and restated 2024 equity incentive plan of the Company (Plan).

We are furnishing this opinion as Exhibit 5.1 to the Registration Statement.

OUR REVIEW

For the purposes of giving this opinion we have examined and relied upon the documents listed in Part 1 of Schedule 1 (Documents). We have not examined any other documents, even if they are referred to in the Documents.

In giving this opinion we have relied upon and assume the accuracy and completeness the Register of Directors and Officers (each as defined in Part 1 of Schedule 1), the contents of which we have not verified.

We have not made any other enquiries concerning the Company and in particular we have not investigated or verified any matter of fact or opinion (whether set out in any of the Documents or elsewhere) other than as expressly stated in this opinion.

Unless otherwise defined herein, capitalised terms have the meanings assigned to them in Schedule 1.

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

LIMITATIONS

Our opinion is limited to, and should be construed in accordance with, the laws of the Cayman Islands at the date of this opinion. We express no opinion on the laws of any other jurisdiction.

This opinion is limited to the matters stated in it and does not extend, and is not to be extended by implication, to any other matters.

This opinion is given solely for the benefit of the Addressee in connection with the matters referred to herein and, except with our prior written consent it may not be transmitted or disclosed to or used or relied upon by any other person or be relied upon for any other purpose whatsoever, save as, and to the extent provided, below.

A copy of this opinion may be provided (a) where required by law or judicial process and (b) for the purpose of information only, to the Addressee’s affiliates, professional advisers, auditors, insurers and regulators.

ASSUMPTIONS AND RESERVATIONS

We give the following opinions on the basis of the assumptions set out in Schedule 2 (Assumptions), which we have not verified, and subject to the reservations set out in Schedule 3 (Reservations).

OPINIONS

	1.	Incorporation: The Company is an exempted company incorporated with limited liability and existing under the laws of the Cayman Islands and is a separate legal entity.

	2.	Authorised Share Capital: Based solely on our review of the Constitutional Documents, the authorized share capital of the Company is 50,000,000,000 shares of US$0.00001 each, comprising 49,500,000,000 Class A ordinary shares of a par value of US$0.00001 each and 500,000,000 Class B ordinary shares of a par value of US$0.00001 each.

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

	3.	Authorisation: The Company has taken all necessary corporate action to authorise the issuance of the Offering Shares under the Registration Statement.

	4.	Issue of Shares: The Offering Shares to be allotted and issued by the Company have been duly authorised, and when fully paid, allotted and issued by the Company in the manner set out in the Plan and in accordance with the Resolutions, will be validly issued, fully paid and non-assessable. The reference in this opinion to Offering Shares being non-assessable shall mean solely that no further sums of money are required to be paid by the holders of such Offering Shares in connection with the issuance thereof.

CONSENT

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In providing our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities the Securities Act of 1933 of the United States of America (as amended) or the Rules and Regulations of the Commission thereunder.

Yours faithfully

Appleby

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

Schedule 1

Part 1

Documents Examined

	1.	A copy of the certificate of incorporation of the Company dated 18 August 2022 and a copy of the certificate of incorporation on change of name of the Company dated 27 October 2022, each issued by the Registrar of Companies (Certificate of Incorporation).

	2.	A scanned copy of the amended and restated memorandum of association and articles of association of the Company adopted on 2 October 2026 (together the Constitutional Documents).

	3.	A copy of the written resolutions of the board of directors of the Company dated 12 October 2026 (Resolutions).

	4.	A scanned copy of the register of directors and officers of the Company provided to us on 27 April 2026 (Register of Directors and Officers).

	5.	A copy of the registration statement on Form S-8 dated 28 October 2026.

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

Schedule 2

Assumptions

We have assumed:

	1.	(i) that the originals of all documents examined in connection with this opinion are authentic, accurate and complete; and (ii) the authenticity, accuracy, completeness and conformity to original documents of all documents submitted to us as copies;

	2.	that there has been no change to the information contained in the Certificate of Incorporation and that the Constitutional Documents remain in full force and effect and are unamended;

	3.	that the signatures, initials and seals on all documents and certificates submitted to us as originals or copies of executed originals are authentic, and the signatures and initials on any Document executed by the Company are the signatures and initials of a person or persons authorised by the Company, by resolution of its board of directors or any power of attorney granted by the Company, to execute such Document;

	4.	that where incomplete documents, drafts or signature pages only have been supplied to us for the purposes of issuing this opinion, the original documents have been duly completed and correspond in all material respects with the last version of the relevant documents examined by us prior to giving our opinion;

	5.	the truth, accuracy and completeness of all representations and warranties or statements of fact or law (other than as to the laws of the Cayman Islands in respect of matters upon which we have expressly opined) made in the Documents and any correspondence submitted to us;

	6.	the accuracy, completeness and currency of the records and filing systems maintained at the public offices where we have searched or enquired or have caused searches or enquiries to be conducted, that such search and enquiry did not fail to disclose any information which had been filed with or delivered to the relevant body but had not been processed at the time when the search was conducted and the enquiries were made;

	7.	that the Company was not (or, upon execution will not be) unable to pay its debts as they became due when it approved the Plan and the issuance of the Offering Shares and did (or will) not become unable to do so as a result of the approval of the Plan and the issuance of the Offering Shares or the performance of its obligations thereunder;

that none of the Company’s directors or its registered office has received any notice of any litigation or threatened litigation to which the Company is or may be party ;

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

	9.	that the Company has not (i) received notice of any stop notice under Order 50 of the Grand Court Rules in respect of any of its shares or (ii) received notice of any restrictions notice under the Beneficial Ownership Transparency Act (as amended) of the Cayman Islands in respect of any of its shares, which restrictions notice has not been withdrawn by the registered office or ceased by court order;

	10.	that (i) any meetings at which the Resolutions were passed were duly convened and had a duly constituted quorum present and voting throughout, (ii) all interests of the directors of the Company on the subject matter of the Resolutions, if any, were declared and disclosed in accordance with the law and Constitutional Documents, (iii) the Resolutions have not been revoked, amended or superseded, in whole or in part, and remain in full force and effect at the date of this opinion, and (v) the directors of the Company have concluded that the Plan and such other documents approved by the Resolutions and the transactions contemplated thereby are bona fide in the best interests of the Company and for a proper purpose of the Company;

	11.	that the Register of Directors and Officers accurately reflects the names of the directors and officers of the Company as at the dates the Resolutions were passed or adopted and as at the date of this opinion;

	12.	that there is no matter affecting the authority of the directors of the Company to effect entry by the Company into the Resolutions or the approval of the Plan and the issuance of the Offering Shares including breach of duty, lack of good faith, not disclosed by the Constitutional Documents or the Resolutions, which would have any adverse implications in relation to the opinions expressed herein;

	13.	that there are no records of the Company, agreements, documents or arrangements other than the Constitutional Documents, the Resolutions and the documents expressly referred to herein as having been examined by us which materially affect, amend or vary the transactions contemplated in the Resolutions or restrict the powers and authority of the directors of the Company in any way which would affect opinions expressed herein;

	14.	that the approval of the Plan and the issuance of the Offering Shares and carrying out each of the transactions referred to therein will not conflict with or breach any applicable economic, anti-money laundering, anti-terrorist financing or other sanctions;

	15.	that any applicable escrow conditions have been met;

	16.	that the transactions contemplated by the Plan and the issuance of the Offering Shares are private acts for commercial purposes and not sovereign acts; the property against which enforcement is to be taken or sought to be taken is used or intended to be used for commercial purposes only; and

	17.	that the directors or members of the Company have not taken any steps to have the Company struck off or placed in liquidation, no steps have been taken to wind up the Company and no receiver has been appointed over any of the Company’s property or assets.

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen

Schedule 3

Reservations

Our opinion is subject to the following:

	1.	Preferences: Every conveyance or transfer of property, or charge thereon, and every payment obligation and judicial proceeding, made, incurred, taken or suffered by a company at a time when that company was unable to pay its debts within the meaning of section 93 of the Companies Act (as amended) of the Cayman Islands (Companies Act), and made or granted in favour of a creditor with a view to giving that creditor a preference over the other creditors of the company, would be voidable upon the application of the company’s liquidator pursuant to section 145(1) of the Companies Act, if made, incurred, taken or suffered within the six months preceding the commencement of a liquidation of the company. Such actions will be deemed to have been made with a view to giving such creditor a preference if it is a “related party” of the company. A creditor shall be treated as a related party if it has the ability to control a company or exercise significant influence over a company in making financial and operating decisions.

	2.	Undervalues: Any disposition of property made at an undervalue by or on behalf of a company and with an intent to defraud its creditors (which means an intention to wilfully defeat an obligation owed to a creditor), shall be voidable (i) under section 146 of the Companies Act at the instance of the company’s official liquidator, and (ii) under the Fraudulent Dispositions Act (as amended) of the Cayman Islands, at the instance of a creditor thereby prejudiced.

	3.	Defrauding Creditors: If any business of a company has been carried on with intent to defraud creditors of the company or creditors of any other person or for any fraudulent purpose, the Cayman Islands court may declare that any persons who were knowingly parties to the carrying on of the business of the company in such manner are liable to make such contributions, if any, to the company’s assets as the court thinks proper.

	4.	Corporate Documents: The Registry of Companies in the Cayman Islands is not public in the sense that copies of the Constitutional Documents and information on shareholders is not publicly available and information on directors is limited. We have therefore obtained scanned copies of the corporate documents specified in Schedule 1 and relied exclusively on such scanned copies for the verification of such corporate information.

Bermuda ■ British Virgin Islands ■ Cayman Islands ■ Guernsey ■ Hong Kong ■ Isle of Man ■ Jersey ■ Mauritius ■ Seychelles ■ Shanghai ■ Shenzhen