There is no clean way to detect when a barb camp is cleared nor is there a way to workaround it with only lua. There is no event you can use (the improvement destroyed event is UI related, not game play related) and trying to calculate where camps are and polling each turn to see if they are gone is full of corner cases (ranged attack kills the unit but not the camp, expanding city tiles clears the camp but not the unit, etc).
You can do it with a custom dll but that is probably not worth it.