Apart from the CTM routine, one thing which should not be neglected is exfoliation. Yes, you should exfoliate regularly even if your skin is dry. Twice a week with a gentle exfoliator is good idea. Natural apricot scrubs are a good option or using besan is also another good option. They are gentle and would not harm the skin. And, moisturize repeatedly. Buy a good body lotion which is thick enough like probably Nivea classic might suit you or some other intensive body lotion. Do not have a bath in extremely hot water.
Another good option is oil massage for the body using almond oil or coconut oil or sesame oil once or twice a week. That will moisturize the body very well and also simultaneously exfoliate your skin. Oil is a very good option for removing the flaky skin which is generally a reason for dry skin. Also, while massaging your body, be sure to apply oil in the belly button as it is somehow magically linked to soft lips.
Coming to cracked lips, exfoliate twice a week using the tooth brush or this lip scrub . And, always use a lip balm. Well, I would say don't go for vaseline but go for shea butter or cocoa butter based lip balms. If you are able to find them, well and good. Otherwise, a simple nightly treatment for your lips is to apply a tablet of Evion (Vitamin E) daily on your lips and massage them. Also, include your face in this treatment.
Coming to health reasons, now, you might have naturally a very dry skin for which you can actually visit a dermatologist. The doc will get a few blood tests done and probably would be able to tell you even without the blood tests what is wrong with your skin. So, in case, all the above treatments don't work, go to a dermatologist in 2-3 weeks time. Don't ignore.
And, don't forget, hot temperatures and extreme humidity can also cause dryness of the skin so always keep your skin hydrated from the inside.