Re: apple cider vinegar or athletes foot cream might work better

If this works it could be because the peeling of the lips was caused by fungus/yeast. Fungus takes a while to heal because it has to be suppressed during skin cell reproduction AT ALL TIMES, otherwise a few fungus cells can quickly spread and infect other areas.

For instance there is a cure for fungal infected toenails that requires a daily soaking in vinegar, the vinegar inhibits fungus but only the fungus on the outer layers of the skin or nails. The deeper layers are still infected and the vinegar can't penetrate deep enough to get to them. So each day as the old skin comes to the surface and the other layers make their way to the surface one must continually reduced/kill them with the vinegar. If one forgets to do a soaking even for one day the fungus regains control and one must essentially "start over" with the treatment. The secret is that there are many deeper layers of skin cells that have been infected with yeast/fungus and one must inhibit them from infecting each new layer as the skin cells renew. Once the old infected skin cells have been replaced over a period of time with new uninfected skin cells then the peeling lips (infected toenails, athletes foot etc) should go away. I would suggest in addition to lemon that you might also apply apple cider vinegar.
Perhaps even an athletes foot cream would work?

It is important that during this healing time that ones nutrition be adequate for creating healthy strong skin cells that can resist fungal and bacteria infection. The lips were infected (if this is the case) for some reason and the only real reason is that the body did not have a strong enough immune system or did not have the correct nutrition. (one in the same thing).

Probiotics should be taking during this healing time too.