Poor little guy!
If he has LI, he should heal pretty quickly.
What kind of lotions are you using on him? Maybe you need something "stronger" around his mouth to keep the skin more moist so he can open his mouth without it hurting.
Aquaphor and vaseline should work, just keep putting it on constantly. The Vaseline comes in a little tube you can squeeze out and apply directly around the mouth. At 3, maybe let your son do it himself. If he gets it all around his mouth, you don't need to worry, because that's the point!