I don't think this should be labelled a cure because the OP still has peeling lips to a lesser degree.
I think restricting the grains is a total red herring. It sounds as though the lips were on the way to healing themselves and are still in the process of healing. There is nothing to suggest this is anything other than a placebo effect. It is very common to see people making progress with their EC during a change they have made to their lifestyle, the trouble is often they change many things at once so it's next to impossible to determine what, if anything, made a difference.
It would be useful to know more from the OP ; whether they are still picking/biting the lips. More information is needed.