That's why using Antibiotics (like Fucidin) is recommended (e.g. in MikePylons treatment), to prevent getting secondary infections. He didn't use it to fight an existing infection, but to prevent one from happening (because of course the fragile skin and the build up on our lips is a perfect ground for those secondary infections).
If some of us might have or might get fungal infections, it might be necessary to use antifungals while doing "moist healing". Maybe even a combination of Antibiotics and antifungals, and saline solution & water to clean the lips as gently as possible.
I don't think you will be able to get "the right time to exfoliate manually". You should let the skin exfoliate by itself, and do your best to prevent a secondary infection (and of course to get rid off any existing one).