The winner in a fight between a lion and a bear would depend on the species of the bear and lion fighting, but in general, the bear would win. Bears are generally larger and stronger, and lions have thin skulls that can be crushed easily.
According to History Banter, North and Central American settlers in the 1800s arranged fights between grizzly bears and African lions. The grizzlies usually won. Polar bears were also often matched against lions and did not fare so well generally. Mountain lions, while not a true lion, typically lose to black and brown bears. In one notable case, a hiker in California was saved from a mountain lion attack by an angry mother bear who thought the cat was a threat to her cubs, according to The Huffington Post.