Today, my lips are fine. I don't do any treatments specific to peeling lips, though I usually put just a bit of an herbal aloe salve around my mouth after shaving (to keep it that way).
I do notice that if i don't eat to well, or eat too many carbs, i start to get dry skin in various areas, so something to watch out for.
In my opinion, the answer for EC is the same as so many other health issues, and that is, EC is an indication of deeper issues in body, especially the digestive tract. And that can be from many causes. so the "cure" will not be the same for everyone, except in the general sense of needing to work holistically to heal the body, and clear out whatever ails it.
Diet, avoiding food allergens, toxic foods, anything you can do that is good for your entire body, will help this condition, until it just goes away, and the skin heals.