EXHIBIT 5.1

FACSIMILE DIRECT DIAL

February 6, 2024

Lucid Diagnostics Inc.

360 Madison Avenue, 25^th Floor

New York, NY 10017

Ladies and Gentlemen:

Reference is made to the Registration Statement on Form S-8 (the “Registration Statement”) filed by Lucid Diagnostics Inc., a Delaware corporation (“Company”), under the Securities Act of 1933, as amended (the “Act”), with respect to an aggregate of 2,680,038 shares (the “Shares”) of common stock, par value $.001 per share (“Common Stock”), newly reserved for issuance by the Company under the Company’s Amended and Restated 2018 Long-Term Incentive Equity Plan (the “Plan”), pursuant to amendments to the Plan approved by the Company’s stockholders and pursuant to Section 3.1 of the Plan and the duly approved resolutions of the Company’s Board of Directors.

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinion set forth below. With respect to such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as reproduced or certified copies, and the authenticity of the originals of those latter documents. As to questions of fact material to this opinion, we have, to the extent deemed appropriate, relied upon certain representations of certain officers and employees of the Company.

In our examination of documents for purposes of this opinion, we have assumed, and express no opinion as to, the authenticity and completeness of all documents submitted to us as originals, the genuineness of signatures on documents reviewed by us, the conformity to originals and the completeness of all documents submitted to us as copies, the legal capacity of all parties executing any documents (other than the Company), the lack of any undisclosed termination or modification or waiver of any document, the absence of any extrinsic agreements or documents that might change or affect the interpretation or terms of documents, and the due authorization, execution and delivery of all documents by each party thereto other than the Company. We have also assumed that any certificates or instruments representing the Shares, when issued, will be executed by the Company by officers of the Company duly authorized to do so. In rendering our opinion, we have also relied upon a good standing certificate regarding the Company issued by the Delaware Secretary of State and representations and certifications made to us by the Company, including, without limitation, representations that the Company has available a sufficient number of authorized shares of Common Stock that are not currently outstanding or reserved for issuance under other outstanding securities or plans of the Company, to enable the Company to issue and deliver all of the Shares as of the date of this letter. We have also assumed that in granting future awards under the Plan, the Board of Directors of the Company or the appropriate committee thereunder will exercise its discretion in establishing the terms of such awards in accordance with the terms of the applicable Plan and within the permissible limits of the law of the State of Delaware and the certificate of incorporation, as amended, and bylaws, as amended, of the Company.

Based upon and subject to the foregoing, it is our opinion that the Shares, when sold in accordance with the terms of the Plan and the individual instruments or agreements governing their issuance, will be legally issued, fully paid and nonassessable.

The opinion expressed herein is limited to the corporate laws of the State of Delaware, and we express no opinion as to the effect on matters covered by this letter of the laws of any other jurisdiction.

We hereby consent to the use of this opinion as an exhibit to the Registration Statement, to the use of our name as your counsel and to all references made to us in the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations promulgated thereunder.

Very truly yours,

/s/ Graubard Miller