Not a lip biter, not obsessive about them. I was trying to beat a weird finger infection - 2 courses of doxycycline, 1 of bactrim, had just been put on bactrim + levaquin. I had what might have been an allergic reaction to that combo. Not clear because a hand surgeon pulled me off that combo a day later and put me on Sporanox (serious anti-fungal).
Between the 4th Antibiotic and the antifumgal I got very dehydrated & my lips seemed very chapped. Instead of returning to normal in a day or two, they started peeling off. Thin layers, scale-like... relentless for months. Dentist suggested L-lysine, which in my case made a huge difference. Had to stay on it for quite a while and taper off to avoid relapse. Added stress formula B-vitamins in case of B-deficiency... Have had no trouble (and taken no lysine) since Spring.