I too get gunk on my lips in the morning. I wonder if this stuff is mucus, the gooey stuff found throughout the inner body? It's used by the body to fight microorganisms sometimes, but if there's a lot of it being produced it can become a breeding ground for them too. Maybe it is just saliva or whatever, but there are mucus membranes in the lips and it might be worth asking doctors. Mucus wikipedia: http://en.m.wikipedia.org/wiki/Mucus
Mucus and bacteria: http://textbookofbacteriology.net/innate_3.html