My lips get to be pretty bad if I let them dry out. Aside from the skin building up like usual, the difference when I don't put stuff on is it doesn't come off, and it starts to hurt because it hardens and thickens. But maybe if you're forced not to use it your lips will heal on their own, and maybe you're unwittingly doing something that's causing it that you won't continue to do while in service.
What is it about the lip balm that's contraband.. do they not let you bring any kind of cosmetic products or does it have to be for a medical reason? Like what if it was something like Aquaphor?