The three lights on the ceiling fan are not working well. One won't stay on, one makes a
Pop sound and one is working correctly. Does this mean it needs to be replaced?

Try the good bulb in each of the sockets, look inside the sockets for burnt or corroded, Remove light and see if you can see/test the problem, no luck, replace.
I wouldn't remove until you are about to go to the supply house to minimize down time.