We are acting as counsel to LXP Industrial Trust, a Maryland real estate investment trust (the “Company”), in connection with the issuance and sale of $300,000,000 aggregate principal amount of the Company’s 6.750% Senior Notes due 2028 (the “Notes”) pursuant to a registration statement on Form S-3 (File No. 333-253297) (the “Registration Statement”), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), on February 19, 2021, and the prospectus dated February 19, 2021 (the “Prospectus”), as supplemented by the supplement to the Prospectus dated November 2, 2023 (the “Prospectus Supplement”). The Notes are to be issued pursuant to an Indenture dated as of May 9, 2014, between the Company and U.S. Bank National Association (the “Indenture”), as supplemented by the Fourth Supplemental Indenture (the “Supplemental Indenture”) to be entered into between the Company and U.S. Bank Trust Company, National Association (a successor in interest to U.S. Bank National Association) as trustee (the “Trustee”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

Hogan Lovells US LLP is a limited liability partnership registered in the state of Delaware. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante Amsterdam Baltimore Beijing Birmingham Boston Brussels Colorado Springs Denver Dubai Dusseldorf Frankfurt Hamburg Hanoi Ho Chi Minh City Hong Kong Houston Johannesburg London Los Angeles Luxembourg Madrid Mexico City Miami Milan Minneapolis Monterrey Munich New York Northern Virginia Paris Philadelphia Rome San Francisco São Paulo Shanghai Silicon Valley Singapore Sydney Tokyo Warsaw Washington, D.C. Associated Offices: Budapest Jakarta Riyadh Shanghai FTZ Ulaanbaatar. Business Service Centers: Johannesburg Louisville. Legal Services Center: Berlin. For more information see www.hoganlovells.com

For purposes of this opinion letter, we have assumed that (i) the issuance, sale, amount and terms of the Notes have been duly authorized and established by proper action of the Board of Trustees of the Company or a duly authorized committee of such board consistent with the procedures and terms described in the Registration Statement and in accordance with the Company’s declaration of trust and bylaws and applicable Maryland corporate law, in a manner that does not violate any law, government or court-imposed order or restriction or agreement or instrument binding on the Company or otherwise impair the legal or binding nature of the obligations represented by the applicable Notes, (ii) the Trustee under the Indenture, to be supplemented by the Supplemental Indenture, upon execution of the Supplemental Indenture, will have all requisite power and authority under all applicable laws, regulations and governing documents to execute, deliver and perform its obligations under the Indenture and the Supplemental Indenture and has complied with all legal requirements pertaining to its status as such status relates to the Trustee’s right to enforce the Indenture and the Supplemental Indenture against the Company, (iii) the Trustee has authorized, executed and delivered the Indenture and has authorized and will duly execute and deliver the Supplemental Indenture, (iv) the Trustee is validly existing and in good standing in all necessary jurisdictions, (v) the Indenture constitutes and, upon its execution, the Supplemental Indenture will constitute valid and binding obligations, enforceable against the Trustee in accordance with their terms, (vi) there has been no, and in the case of the Supplemental Indenture, there will be no mutual mistake of fact or misunderstanding, or fraud, duress or undue influence, in connection with the negotiation, execution or delivery of the Indenture or the Supplemental Indenture, and the conduct of all parties to the Indenture and, upon execution, the Supplemental Indenture has complied and will comply with any requirements of good faith, fair dealing and conscionability, and (vii) there are, have been and will be no agreements or understandings among the parties, written or oral, and there is, has been and will be no usage of trade or course of prior dealing among the parties (and no act or omission of any party) that would, in either case, define, supplement or qualify the terms of the Indenture or, upon its execution, the Supplemental Indenture. We also have assumed the validity and constitutionality of each relevant statute, rule, regulation and agency action covered by this opinion letter.

This opinion letter is based as to matters of law solely on the applicable provisions of the laws of the State of New York (but not including any laws, statutes, ordinances, administrative decisions, rules or regulations of any political subdivision below the state level), as currently in effect. We express no opinion herein as to any other statutes, rules or regulations (and in particular, we express no opinion as to any effect that such other statutes, rules or regulations may have on the opinion expressed herein).

Based upon, subject to and limited by the foregoing, we are of the opinion that, following (i) receipt by the Company of the consideration therefor specified in the Underwriting Agreement dated November 2, 2023, by and among the Company, Wells Fargo Securities, LLC, J.P. Morgan Securities LLC, Mizuho Securities USA LLC and each of the other underwriters named in Schedule I thereto and (ii) the due execution, authentication, issuance and delivery of the Notes pursuant to the terms of the Indenture and the Supplemental Indenture, and as contemplated by the Prospectus Supplement, the Notes will constitute valid and binding obligations of the Company.

The opinion expressed above with respect to the valid and binding nature of obligations may be limited by bankruptcy, insolvency, reorganization, receivership, moratorium or other laws affecting creditors’ rights (including, without limitation, the effect of statutory and other law regarding

fraudulent conveyances, fraudulent transfers and preferential transfers) and by the exercise of judicial discretion and the application of principles of equity, good faith, fair dealing, reasonableness, conscionability and materiality (regardless of whether the Notes are considered in a proceeding in equity or at law).

This opinion letter has been prepared for use in connection with the filing by the Company of a Current Report on Form 8-K on the date hereof (the “Form 8-K”), which Form 8-K will be incorporated by reference into the Registration Statement and the Prospectus Supplement, and speaks as of the date hereof. We assume no obligation to advise of any changes in the foregoing subsequent to the delivery of this opinion letter.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Form 8-K, and to the reference to this firm under the caption “Legal Matters” in the Prospectus Supplement constituting a part of the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Act.