Why would a lion win a fight against a black bear?

Most of the time, it wouldn't. The black bear is bigger (700 lbs vs 550 lbs), stronger (bears are, pound for pound, the strongest of the order Carnivora, an order containing both bears and felines) and smarter (if food is a reward, they can even learn faster than chimpanzees) than the lion. The black bear has stronger forequarters (it can flip a flat-shaped rock more than twice its own weight) and jaws (1500 lbs vs 1000 lbs, the black bear uses its bite to rip through wood). The lion is slightly faster (30 mph vs 35 mph) but the black bear is better designed for a fight. Here's an excerpt from The Great Bear Almanac...

"There is also a vague account of a circus (African) lion that jumped an American black bear during an act. The fight was fierce and both combatants were injured, but the lion's injuries were of the extent that it had to be destroyed."