Exhibit 32.1

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, 2013 as filed with the Securities and Exchange Commission on the date hereof, I, T. Wilson Eglin, President (principal executive 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/ T. Wilson Eglin

T. Wilson Eglin

President (principal executive officer) of Lex GP-1 Trust,

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

March 17, 2014