Why does the skin on chapped and dry lips stick your lips together? (As in when you close your mouth)
The dry lips have dried saliva, when that saliva gets wet again the dried one will try to absorve it, if you close your mouth, the fresh saliva layer will be absorbed and merged with the dried one, from the top and bottom lip. That makes them stick.
I always assumed that it was the saliva drying, acting as a kind of glue, but I may be wrong.