I get that from eating certain foods (usually salty things, cheese, or anything rough in texture), and it tends to get worse if I'm not drinking enough. How's your hydration?
I find chocolate (pure chocolate - no biscuity stuff, sugary shells or whatever) and creamy things (milkshakes are good) help. Squishy foods (eg. curry, pasta) are neutral. Cleaning teeth helps a lot. Drinking provides short-term (of the order of seconds) relief. Consequently, I find it's actually an advantage when cycling, as it encourages me to drink more often.
Dry lips are another matter, I tend to get those from too much time in the sun, or being sandblasted in winter. They only correlate if it's an allergic reaction to something I've eaten.