A pill will rarely go down someone's lungs however if the pill does go down your throat and then goes into the wrong pipe then gets stuck in your lung then yes it would dissolve.
However if you do get a pill stuck in your lung then you might have trouble breathing and should see a doctor or go to the emergency room.
The pill stuck in your lungs could cause infection of your lungs and inflammation of your lungs as well.
Most times the pill may actually just be stuck in your throat and not in your lungs even though it can feel like the pill is in your lungs.
The stuck pill should begin dissolving and the feeling should go away within 30 to 60 minutes.