Exhibit 5.1

February 22, 2023

Core Laboratories Luxembourg S.A.

12E Rue Guillaume Kroll

L-1882 Luxembourg

Grand Duchy of Luxembourg

Re: Registration Statement on Form S-4

Ladies and Gentlemen:

We have acted as counsel to Core Laboratories Luxembourg, a public limited liability company incorporated under the laws of Luxembourg (“Core Lab Luxembourg”) and wholly-owned subsidiary of Core Laboratories N.V., a public company with limited liability (naamloze vennootschap) incorporated under Dutch Law (“Core Lab N.V.”), in connection with the domestication in the State of Delaware (the “U.S. Domestication”) of Core Lab Luxembourg as Core Laboratories, Inc., a Delaware corporation (“Core Lab Delaware”), and the related Registration Statement on Form S-4 (the “Registration Statement”) of Core Lab Luxembourg, filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder (the “Rules”). The U.S. Domestication will be effected pursuant to the provisions of Section 388 of the General Corporation Law of the State of Delaware, 8 Del. C. § 388, by filing a certificate of corporate domestication and a certificate of incorporation in respect of Core Lab Delaware with the Secretary of State of the State of Delaware (the “Secretary of State”).

In connection with the U.S. Domestication, Core Lab Delaware will assume (i) Core Laboratories N.V. 2020 Long-Term Incentive Plan (as amended), (ii) the Core Laboratories N.V. 2014 Nonemployee Director Stock Incentive Plan (as amended), (iii) Core Laboratories Supplemental Executive Retirement Plan (as amended), and (iv) the Core Laboratories N.V. Deferred Compensation Plan (collectively, including any schedules or appendices thereto, as amended from time to time, the “Core Lab N.V. Incentive Plans” and following such assumption by Core Lab Delaware, the “Core Lab Delaware Incentive Plans”), and each outstanding stock option (together with any associated tandem stock appreciation right), stock appreciation right, performance share unit, restricted share unit, deferred share unit, restricted stock and other share-based award granted by Core Lab N.V. pursuant to the Core Lab N.V. Incentive Plans (collectively, the “Core Lab N.V. Incentive Awards”) will be exchanged for an incentive award granted by Core Lab Delaware (collectively, the “Core Lab Delaware Incentive Awards”) pursuant to the Core Lab Delaware Incentive Plans. The Core Lab Delaware Incentive Awards will be subject to substantially the same terms and conditions as the Core Lab N.V. Incentive Awards, except, in the case of equity-based Core Lab N.V. Incentive Awards, the securities issuable upon exercise or settlement of the Core Lab Delaware Incentive Awards, as applicable, will be shares of common stock, par value $0.01 per share (“Common Stock”), of Core Lab Delaware (or their cash equivalent) rather than common shares (“Core Lab N.V. Common Shares”) of Core Lab N.V. (or their cash equivalent).

Vinson & Elkins LLP Attorneys at Law Austin Dallas Dubai Houston London Los Angeles New York Richmond Riyadh San Francisco Tokyo Washington 845 Texas Avenue, Suite 4700 Houston, TX 77002 Tel +1.713.758.2222 Fax +1.713.758.2346 velaw.com

Core Laboratories Luxembourg S.A. February 22, 2023 Page 2

You have asked us to furnish our opinion as to the legality of the securities being registered under the Registration Statement. The Registration Statement relates to the registration under the Act of 46,634,027 shares of Common Stock of Core Lab Delaware, consisting of shares of Common Stock of Core Lab Delaware to be issued to holders of Core Lab N.V. Common Shares in connection with the U.S. Domestication (the “Shares”) and shares of Common Stock of Core Lab Delaware that may be issued pursuant to the Core Lab Delaware Incentive Awards (the “Award Shares”).

In connection with the furnishing of this opinion, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (collectively, the “Documents”):

1. the Registration Statement;

2. the Merger Plan, dated as of January 16, 2023 (the “Merger Plan”), between Core Lab N.V. and Core Lab Luxembourg, included as Exhibit 2.1 to the Registration Statement;

3. a draft of the certificate of incorporation of Core Lab Delaware to be filed with the Secretary of State, included as Exhibit 3.1 to the Registration Statement;

4. a draft of the certificate of corporate domestication of Core Lab Delaware to be filed with the Secretary of State;

5. a draft of the bylaws of Core Lab Delaware to be adopted by Core Lab Delaware, included as Exhibit 3.2 to the Registration Statement; and

6. the Core Lab N.V. Incentive Plans and the forms of award agreements (collectively, “Award Agreements”) relating to awards granted under the Core Lab N.V. Incentive Plans.

In addition, we have examined such other certificates, agreements and documents that we deemed relevant and necessary as a basis for the opinions expressed below. We have relied upon the factual matters contained in the representations and warranties of Core Lab N.V. and Core Lab Luxembourg made in the Documents and upon certificates of public officials and officers of Core Lab N.V. and Core Lab Luxembourg.

In our examination of the Documents referred to above, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the documents reviewed by us, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic, reproduced or conformed copies of valid existing agreements or other documents, the authenticity of all the latter documents and that the statements regarding matters of fact in the certificates, records, agreements, instruments and documents that we have examined are accurate and complete.

Core Laboratories Luxembourg S.A. February 22, 2023 Page 3

Based upon the above, and subject to the stated assumptions, exceptions and qualifications, we are of the opinion that:

1. When issued, delivered and paid for as contemplated in the Registration Statement and in accordance with the terms of the Merger Plan, the Shares will be validly issued, fully paid and non-assessable; and

2. When issued, delivered and paid for as contemplated in the Registration Statement and in accordance with the terms of the Merger Plan, the Core Lab Delaware Incentive Plans and any applicable Award Agreement, the Award Shares will be validly issued, fully paid and non-assessable.

The foregoing opinions are limited in all respects to the General Corporation Law of the State of Delaware (including the applicable provisions of the Delaware Constitution and the reported judicial decisions interpreting these laws) and the federal laws of the United States of America, and we do not express any opinions as to the laws of any other jurisdiction.

The foregoing opinions are limited to the matters expressly stated herein, and no opinion is to be inferred or implied beyond the opinions expressly set forth herein. We undertake no, and hereby disclaim any, obligation to make any inquiry after the date hereof or to advise you of any changes in any matter set forth herein, whether based on a change in the law, a change in any fact relating to the Company or any other person or any other circumstance.

We hereby consent to the statements with respect to us under the heading “Legal Matters” in the prospectus forming a part of the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended.

Very truly yours,

           /s/ Vinson & Elkins L.L.P.

           Vinson & Elkins L.L.P.