My experience and knowledge of others has left me with two conclusions:
A) is that when leaving the lips alone, the thick skin is left on and the skin underneath of it is allowed to heal because it is being protected from drying out. The problem now is that eventually its time for the thick skin to fall off, this leaves the newly formed skin underneath exposed once again to the elements causing it to dry up and die, hence repeating the same peeling process over and over. This is why leaving your lips alone has not worked for anyone I believe.
B) is that some sort of malfunction has happened which is preventing the lips from receiving proper moisture, which is causing the skin to dry out, die, and peel.