My friend's son had chapped sore lips year round as well, and they finally found out that he had major allergies to gluten, eggs, dairy and a variety of other foods. They ended up taking him to a naturopath and did extensive tests on him to find out what was causing the problem. Although it took a major change in his diet, his lips have cleared up, and he is no longer getting sick (runny noses, diarreah etc.). They never thought that he had any allergies, and just chalked up the chapped lips to living in a dry climate. I am not sure that this is what is going on with your child, but my friend's son wasn't diagnosed until he was 4.5, so it's possible that your son has the same problem.
If you are uncomfortable taking your child to an alternative doctor, I'm sure you can get him tested for allergies through a traditional doctor as well. I'm not sure how allergists test for allergens (I can't imagine that they still do the old prick test, but I would find out before taking your son). I know that in my friend's case, the doctor's examination did include an extensive blood test.
Perhaps it is just chapped lips due to dry air, and a humidifier will help, but it wouldn't hurt to talk to his pediatrician at the very least.