If your son wants to try salicylic acid, I would suggest trying the milder, easier, cheaper version of it first..... an aspirin mask.
Aspirin IS salicylic acid. You can make your own "mask" (think a ladies facial mask, like a mud mask). To make it, take a few super cheap, plain, UNcoated aspirin, and either in a tiny dish or the palm of your hand, moisten them with a few drops of water at a time until they dissolve, Spread the resulting grainy goo over the area you want to treat. Let it dry for 5-10 minutes, then rinse it off with plain water.
It works great on facial skin, makes it smooth and soft as a baby's bum. It should work equally well on lips.
At least with this version, it won't be super crazy strong like some hardcore salicylic acid, and it will have no added chemical ingredients to complicate the situation. You will also be able to tell if there is any sensitivity to the SA itself. And even if it is not strong enough, you only wasted a dollar for a bottle of ultra cheap aspirin.
[Note: The aspirin MUST be the uncoated kind, or it will not work, because they won't dissolve.]
[NOTE - depending on your son's age, Reyes Syndrome could be an issue with using aspirin]