Exhibit 5.1

May 30, 2025

Lucid Diagnostics Inc.

360 Madison Avenue, 25th Floor

New York, New York 10017

Ladies and Gentlemen:

We have acted as counsel to Lucid Diagnostics Inc., a Delaware corporation (the “Company”), in connection with the preparation of the Registration Statement on Form S-3 (File No 333-268560), filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), which was declared effective on December 6, 2022 (“Registration Statement”), and the offering by the Company pursuant thereto (the “Offering”) of $25,000,000 of the shares of Common Stock covered by the Registration Statement (the “Shares”), from time to time through or to Maxim Group LLC acting as agent or principal (“Sales Agent”), pursuant to a Sales Agreement (the “Sales Agreement”), between the Sales Agent and the Company. Sales in the Offering will be made pursuant to a prospectus supplement and accompanying base prospectus included as part of the Registration Statement (the “Prospectus Supplement”). This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In rendering the opinion set forth below, we have reviewed (a) the Sales Agreement, (b) the Registration Statement and the exhibits thereto and the Prospectus Supplement, (c) the Company’s Certificate of Incorporation and Bylaws, each as amended and restated to date; (d) certain records of the Company’s corporate proceedings as reflected in its minute books; and (e) such statutes, records, and other documents as we have deemed relevant. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, and conformity with the originals of all documents submitted to us as copies thereof. In addition, we have made such other examinations of law and fact as we have deemed relevant in order to form a basis for the opinions hereinafter expressed.

No opinion is expressed herein other than as to the laws of the State of New York, the corporate law of the State of Delaware, and the federal law of the United States of America.

Based upon and subject to the foregoing, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of the Company and, when issued, delivered and paid for in accordance with the Registration Statement and the terms of the Sales Agreement, the Shares will be validly issued, fully paid and nonassessable.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof, and incorporation by reference of this opinion into the Registration Statement. We also consent to the use of our name as counsel to the Company and to all references made to us in the Registration Statement and the Prospectus Supplement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations promulgated thereunder. This opinion is expressed as of the date hereof and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable law.