Hello! I had this problem for so long and I thought it was just that I had very dry skin and it was driving me crazy! I would put neosporin (is that how you spell that? haha) and vaseline on the corners of my lips at night and in the morning most of the time it would still be there.
Finally, for a completely different reason (bad morning headaches, sore throats, etc), I went to my ENT (ear nose and throat) and out of the blue he commented on the cracks and blisters at the corners of my lips. He said it's called angular chelitis. This can be caused by many things, including iron or B12 deficiency, bacterial infection, fungus, dry skin, etc. It can also be caused by not getting enough air when you breathe through your nose, and as a result, you breathe too much through your mouth and it causes angular chelitis. Turns out, mine was being caused because I had a bone spur inside my nose, as well as a severely deviated septum that was causing me to not get enough air at nighttime when sleeping. So, my ENT had me use Breath-rite nose strips for a week at night (seriously, those are amazing) as well as doing a nose spray at night and a different nose spray that he prescribed in the morning for a week. And guess what...the angular chelitis was GONE. A few weeks after that, I had nasal/sinus surgery that removed the bone spur and fixed my septum and I haven't had the problem since.
ANYWAY....so sorry to ramble on like that
But, my point being, if you have any nasal symptoms, sinus, sore throat, headaches, ear symptoms anything like that, maybe you should get checked out by an ENT. Your problem could very likely be being caused by not breathing as well at night as you should be. You could even check yourself by trying the Breath-rite nose strips for a week and Afrin at night for 3 days (that's what he had me do) and see if it helps. If it does, you may have your answer.
Phew!
Good luck!