It can be due to lip licker’s dermatitis or cheilitis skin. If there is any fissuring of the corners of the mouth then angular cheilitis should be ruled out. When the corners of the lips are cracked, bacteria and yeast that are normally present in the mouth can get into those cracks when there is some dripping of saliva at nighttime and cause more inflammation.
I recommend you see your dermatologist for proper treatment, as that may combine an anti-inflammatory, antibacterial and anti-yeast meds and that you use just plain petroleum jelly for moisturizing. This is particularly important right before bedtime.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.