Chapped lips and dry mouth result from poor saliva production and poor thyroid. When your body is working properly, your teeth will actually release liquid which will keep the teeth and gums clean and healthy, when the body is not working properly, the teeth will not release this liquid, and actually draw liquid in, which causes food and junk to stick to the teeth, the mouth to become dry, plaque to form and the gums to recede. When your body is working properly, your skin will be very moist via having a high water content near the surface, it will not be dry and flaky. Oil/sebum does not moisten your skin, by the way.
I first suffered the dry mouth while doing a fruitarian diet. Not sure how to fix.
Ideas I have are that it's nutrient deficiency, either from the foods not having the needed nutrients, or from a poor thyroid struggling to digest these foods.
The combination of fruit and animal foods at the same meal may be an issue for a poor thyroid. Well, that's what the "food combining" diet says. Ever tried separating them? If you get enough sugar your glycogen will be full so that a protein meal won't be an issue.
Sometimes, after a particular meal, my teeth will become clean, white and mouth moist, but I do not really know why yet. I will eat the same meal again and get dirty, sticky teeth and a dry mouth.