What's the PG/VG ratio of your eliquid? Depending on what kind of tank you're using, too much VG can gum up the coil.
VG = thicker liquid, slightly sweeter, more vapor
PG = thinner liquid, more throat hit, less vapor
If you can change the ratio of PG/VG, do it a little at a time, vape to see if that's enough to stop the cracked lips. Also, try to be more conscious of how often you're licking your lips (especially around the corners). Because of the cracking, it might be that you're licking your lips more often therefore exacerbating the problem.