I don't want to state the obvious but crusts don't form in a moist environment. If you keep your lips moist, like you did with water, then the crusts can't form. The crust only form when the lips are dry. Instead of water, just use aquaphor constantly and your lips will be crust free. It probably won't heal your lips but hey, it's a lot better than having those ugly yellow/brown crusts.
Not to discourage you but the leave it alone method won't cure you. If by any chance it does work, it'll take years and even then it still might not work. Why go through all that kind of hell if there's a better and quicker way to get cured?
Yes, there is a way to heal your lips but leaving them alone is definitely not the answer.