It certainly can't hurt to try this method, but dampening your lips with a moist paper towel is not really going to moisturize them for more than a few minutes, imho.
I also think Longterm made a good point about using bottled water to do it, if you try this. Bottled spring water would be best, as it should have no added chemicals, and you can buy it in gallon jugs for less than a dollar at the grocery store. Tap water has chemicals in it that could be contributing to the whole problem in the first place.
This also made me think of another possible contributing factor.... basic hydration. How much water do you guys drink daily? And I do mean WATER, not soda, or sports drinks, or coffee, or beer. When I would get dehydrated, my lip issues always got much worse. Making sure you drink enough water every day is another easy and inexpensive step to take that has only benefits and no potential down side (even if it does not cure your lips).
We should all be drinking at least 8 glasses of water a day, every day. If your lips are dried out and crusting and peeling, there is no possible way that your body being dehydrated is going to be beneficial. It will surely only make things worse.