Exhibit 5.1

June 28, 2024 Tamboran Resources Corporation Suite 01, Level 39, Tower One, International Towers Sydney 100 Barangaroo Avenue, Barangaroo NSW 2000	300 Colorado Street, Suite 2400 Austin, TX 78701 Tel: +1.737.910.7300 Fax: +1.737.910.7301 www.lw.com FIRM / AFFILIATE OFFICES
	Austin	Milan
	Beijing	Munich
	Boston	New York
	Brussels	Orange County
	Century City	Paris
	Chicago	Riyadh
	Dubai	San Diego
	Düsseldorf	San Francisco
	Frankfurt	Seoul
	Hamburg	Silicon Valley
	Hong Kong	Singapore
	Houston	Tel Aviv
	London	Tokyo
	Los Angeles	Washington, D.C.
	Madrid

Re: Registration Statement on Form S-8 with respect to 1,600,000 shares of common stock, par value $0.001 per share

To the addressee set forth above:

We have acted as special counsel to Tamboran Resources Corporation, a Delaware corporation (the “Company”), in connection with the preparation and filing by the Company on the date hereof with the Securities and Exchange Commission (the “Commission”) of a Registration Statement (the “Registration Statement”) on Form S-8 under the Securities Act of 1933, as amended (the “Act”), relating to the issuance of up to 1,600,000 shares of common stock of the Company, par value $0.001 per share (the “Shares”), which may be issued pursuant to the Company’s 2024 Incentive Award Plan (the “2024 Plan”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus, other than as expressly stated herein with respect to the issue of the Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, when the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the recipients and have been issued by the Company for legal consideration therefor (not less than par value) in the circumstances contemplated by the 2024 Plan, assuming in each case that the individual issuances, grants or awards under the 2024 Plan are duly authorized by all necessary corporate action and duly issued, granted or awarded and exercised in accordance with the requirements of law and the 2024 Plan (and the agreements duly adopted thereunder and in accordance therewith), the issue and sale of

June 28, 2024

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the Shares will have been duly authorized by all necessary corporate action of the Company, and such Shares will be validly issued, fully paid and non-assessable. In rendering the foregoing opinion, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Sincerely,

/s/ Latham & Watkins LLP