Odds are we don't all have the same underlying issue.
My dentist & I think my case was viral due to the timing of the onset and the dramatic response to the L-lysine. The research on herpes & lysine suggest that it's the balance of arginine & lysine which impacts viral replication. High arginine to lysine encourages replication. High lysine to arginine stops replication.
Peeling lips can also be symptom of riboflavin deficiency. (there are over 40 things that have "peeling lips" as a symptom on wrongdiagnosis.com)
There is also always the possibility that it's an eczema/dermatitis thing made worse by stress and certain weather conditions.
I think the people who have bitten/picked/chewed their lips may have triggered an exaggerated response to injury. A cellular hyperplasia type response. Like the lips are trying to make a callus to protect themselves but it doesn't take.