Hm, I don't think they will. I'm pretty sure LV gift cards are to be used at LV boutiques and counters only. I could be wrong though so wait for another member to reply!
LV gift certificates can be used at LV stores but not at LV counters inside of department stores. (ex: LV gift cert. can't be used at the Bloomingdale's LV counter - I've asked this question directly at Bloomingdale's.)