Lurker here who actually came out of hiding because this question was so relevant to my experience.
To answer your question, I've been leaving them completely alone for 16(!) months now. By completely alone, I mean I let the lips peel and fall off by themselves, and literally nothing touches them except for water when I brush my teeth twice a day, and mouthwash when I rinse with it once a day. I take extreme care to avoid getting water on my lips when I shower, and I drink everything out of a straw. I also cut my food into small pieces so I don't inadvertently tear my lips when I try to bite something.
I should clarify though that I haven't left them alone for 16 months straight. Every 1-2 months I've been prematurely peeling them and putting vaseline lip therapy on them to make them look 'normal' when I've had to go home for breaks, visit family, etc. Whenever I did this it seemed to set my progress back, but not irreversibly so.
Anyway, over these 16 months, I've actually seen noticeable healing. When I first started leaving them alone, after brushing my teeth and not putting anything on them they would immediately dry out and form hard, thick crusts. These crusts were huge and even formed "air pockets" that you could press down on. When they separated from my lips, they would stick out at an angle. When they got close to falling off, they would hang off my lips.
But month by month, my lips got better. The first sign of change I noticed was that the peels seemed to be getting a bit thinner. They also started to no longer form air pockets or stick out at an angle after peeling. They were becoming thin enough that they would "hug" the contours of my lips even after they separated. Another major sign of change I observed was that the fresh skin after a peel had fallen off would now stay reddish and normal-colored for a few days. In the past, the new skin would turn white almost immediately when water touched it.
Today, the peeling is so thin that it's translucent. Even after the skin hardens, it stays reddish because the peel is so thin and transparent. It takes about 3-4 days before it separates and becomes noticeable, and as I said earlier it no longer juts out or hang off my lips, it just sits directly on top of the skin until it's ready to fall off. Also, the new skin takes a day or two to harden now, even after touching water. In the past, it would harden within minutes.
I can't claim that I'm cured using this method, because I'm not yet. But there has been objective, undeniable change in my lips since I started leaving them alone. And if I hadn't manually peeled them every month or two to avoid embarrassment when I had to see people, it's likely they'd be in even better shape now. I can't guarantee that this will work for you or anyone else, but I am proof that at least one person has seen moderate success following this method. If you have the luxury of avoiding social contact for a long time, or the mental strength to not give a f***, I'd give this a shot for a good 2-3 months and see how it works for you. Good luck.