Yes, according to me, the cause is either internal or an infection.
I can explain this never-ending peeling cycle by a lack of vitamins/minerals/trace elements or the infection by any virus, bacteria, parasite or fungus which had infected lips during the picking period when it was chapped.
Also, I think as you that lipstick, oitnment, lipbalm are useless and just hide the problem without healing it. It acts as an 'overnutrition' which drown the lips and prevent it to regenerate itself properly...BUT in the absence of a solution it's a way to handle the situation and avoid to have ugly corn flakes on the face.
Frankly, I'm following the state of my lips and I'm always surprised of being unable to know if it healed or not. If I say that it's because two days ago my lips became smoothes and now, after having left my lips free for night, it seems to be healed because I can perfectly see the grooves and the texture difference between inside-outside...still have to know when it will peel again! -unless I'm cured, it would be too good to be true-
I agree your point of view about the food, its chemicals and perservatives but we always live in this kind of food and nowadays it's very -very- hard, perhaps expensive, to convert our entire alimentation to a 100% bio one.
Otherwise, have you any pictures to see your improvement?!