Dehydrated skin and lips are connected to two root causes in your body. One, weak liver and second, gut fermentation.
First thing I would do with severe case of dry lips and skin is take one tablespoon of castor oil in hot tea, be prepared to go to the bathroom, you will have a diarrhea. Then eat more fiber in your diet, no meats and sugary stuff. Take probiotics like kimchi, sauerkraut, even pay lose are ok. Drink plenty water.
One week later do a liver flush, this will take the burden from your skin.
You are lacking Magnesium, take 200mg Calcium and 500mg Magnesium together daily. Also take Zinc and Biotin.