you will get people who say leaving it alone is the only way to heal it and you will get people who say moisturizing does nothing but good
One of the many dermotologists i went to even told me that it is unlikely that the lips will be able to heal at all when they are that dry, and the only way you have a shot at healing them is to keep them moisturized - not that i believe him, just showing that people will feel strongly about moisturizing
if you've got the time id suggest not applying anything to them, keep that going for as long as you possibly can. wet them throughout the day with water. it seems thats your safest bet, keep in mind Daniel Miller has been doing it for a long time and is still not healed, but he has seen progress slowly but surely
personally, i started applying small amounts of avocodo oil on my lips not more than once a day and the scabs are coming off a bit faster so im not sure if its a good thing.