I have one that does the same thing from post nasal drip.....You need to have an evaluation to see if he might be dealing with a sinus infection, first. Otherwise, allergies can trigger it and an Antihistamine can be prescribed by your Vet.....Karla
Another really benign thing that can cause lip-licking is something stuck between the teeth. I don't know if your dog plays with sticks....or retrieves toys in grass....etc, but tiny fragments of tough grass or pieces of wood can get stuck between teeth and sometimes don't come out very easily. If he eats pretty normally, and seems OK with food, that could be the cause.
Check his mouth thoroughly before you visit the vet.If you can get someone to hold him still and hold his mouth open so you can look properly, so much the better
Toothache is one possibility. Nausea is another. Dogs will lick their lips incessantly if they are nauseous. How is his appetite? Does he seem like he wants to eat but can't? If he's nauseous he won't be interested in food but if it's his tooth, he may act like he wants to eat and will start to eat but then he'll stop and kind of push his food around. I would make an appointment with the vet to have him checked over. A month is a long time for an animal to go with something that is causing discomfort. See what the vet has to say. Please let us know how he is.
Ghilly