Exhibit 32.4

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Lepercq Corporate Income Fund L.P. (the “Partnership”) on Form 10-K for the period ended December 31, 2017 as filed with the Securities and Exchange Commission on the date hereof, I, Patrick Carroll, Vice President and Treasurer (principal financial officer) of Lex GP-1 Trust, the general partner of the Partnership, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1)The Annual Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)The information contained in the Annual Report fairly presents, in all material respects, the financial condition and results of operations of the issuer.

/s/ Patrick Carroll

Patrick Carroll

Vice President and Treasurer (principal financial officer) of Lex GP-1 Trust,

the general partner of Lepercq Corporate Income Fund L.P.

February 27, 2018