"Their lip will heal. If they are dead then they don't heal." "If you are having problem getting it out then rip it out. It's better than a dead fish" Both were said by Doc Muller and he is correct. He also said that when you are unhooking a fish, when you pull it out of the water start holding your breath. When you can't breath anymore neither can the fish.
I always make it as quick as possible. If there is a hole in the fishes lip then so be it. They do not feel pain as humans do. Plus their lips are all cartilage. It heals. No biggie.
ALWAYS carry a pair of pliers or hemostats for freshwater fish. There is sometimes no way to get the leverage you need with just your fingers.