POWER OF ATTORNEY

     KNOW ALL BY THESE PRESENTS, that each of the undersigned hereby makes,
constitutes and appoints Eric D. Marsh, Wayne B. Stoltenberg and Jonathan C.
Curth, signing singly, the undersigned's true and lawful attorneys-in- fact,
with full power and authority as hereinafter described on behalf of and in the
name, place and stead of the undersigned to:

     (i)   execute for and on behalf of the undersigned, in the undersigned's
           capacity as a director, director nominee, officer or beneficial owner
           of shares of common stock (the "Shares") of Vine Energy Inc., a
           Delaware corporation (the "Company"), any Schedule 13D or Schedule
           13G, and any amendments, supplements or exhibits thereto (including
           any joint filing agreements) required to be filed by the undersigned
           under Section 13 of the Securities Exchange Act of 1934, as amended,
           and the rules and regulations promulgated thereunder (the "Exchange
           Act"), and any Forms 3, 4, and 5 and any amendments, supplements or
           exhibits thereto required to be filed by the undersigned under
           Section 16(a) of the Exchange Act;

     (ii)  do and perform any and all acts for and on behalf of the undersigned
           which may be necessary or desirable to complete and execute any such
           Schedule 13D, Schedule 13G, Form 3, 4, or 5 and timely file such
           forms with the United States Securities and Exchange Commission and
           any stock exchange on which the Shares are then listed; and

     (iii) take any other action of any type whatsoever in connection with the
           foregoing which, in the opinion of such attorneys-in-fact, may be of
           benefit to, in the best interest of, or legally required by, the
           undersigned, it being understood that the documents executed by such
           attorneys-in-fact on behalf of the undersigned pursuant to this Power
           of Attorney shall be in such form and shall contain such terms and
           conditions as such attorneys-in-fact may approve in such attorneys-
           in-fact's discretion.

     The undersigned hereby grants to such attorneys-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorneys-in-fact's substitute or
substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted. The undersigned acknowledges
that the foregoing attorneys- in-fact, in serving in such capacity at the
request of the undersigned, are not assuming, nor is the Company assuming, any
of the undersigned's responsibilities to comply with Section 13 and Section 16
of the Exchange Act.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file reports or schedules under Section 13
or Section 16 of the Exchange Act with respect to the undersigned's holdings of
and transactions in securities issued by the Company, unless earlier revoked by
the undersigned in a signed writing delivered to the foregoing attorneys-in-
fact.

                                   * * * * *

     IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 30th day of June, 2021.


                                          /s/ John H. Lee
                                          ----------------------------
                                          John H. Lee