Saliva actually causes the skin on our lips, which already extremely thin and sensitive, to break down.
Combine that with any other contributing factors and you’ve got a perfect storm.
This often invites infections like candida (yeast) or bacterial infections, which make the matter worse.

Also, and we know this can be tough: stop licking your lips!
Keeping unflavored lip balm on them at all times can help kick this habit.
This should help to heal the cracks.

If it doesn’t, definitely seek professional guidance from a doctor.