Personally, I think EC lips will heal fast once you eliminate the causative factor. For instance, the person's lips with H. pylori healed quickly once the H. pylori started going away. And my lips healed quickly once my fibroblasts started decreasing (in theory). Other people's lips with contact allergies healed quickly (within1-2 weeks) after they avoided the allergen.
If it takes months to heal EC lips, I think it is because one needs to rid their body of whatever causative factor is causing imbalance. I am telling you it does not take months to heal EC lips although if seems like it should since the lips look so messed up.