You're exactly right! Leaving the lips alone is the ONLY way to cure them. Eating healthy and excercising speeds up the process. But if you continue to pick and peel the seemingly "dead" skin you will never be cure of this.
I created a website http://www.cureforpeelinglips.com
to document my weekly experience with leaving them completely alone. I have had this for four years and my lips were practically raw...so the rebuilding process is going to take a while.
I also made a documentary on this condition on my youtube, if you would like to take a look: