I have had this condition for all my life. It drives me mad. Usually when I try a new treatment it works for a few days and then the effect wears off. For this treatment it took a few days to work.
I have been using Bepanthen cream which is actually a cream for nappy rash. It hasn't completely cured it, but the results are a million times better than I have ever had before. They have completely stopped peeling, I can't get any peel off at all. They have a tiny bit of dry skin on them but I guess if I continually apply it then this may go too. I stopped using it for a few days and realised that the condition had come back. The best thing is that the cream is mega cheap and lasts forever, the only downside is that it doesn't look so good applying a nappy cream to your lips. Might be worth a try for you others though it might work for you too.