Aesop, who lived in Greece in the 6th century BC, is considered to be the greatest teller of fables. They include ‘The Lion and the Mouse’, ‘The Wolf in Sheep’s Clothing’ and ‘The Hare and the Tortoise’. In an Aesop fable a lion, cow, sheep and a goat go hunting. They kill a deer and the lion divides it into four equal parts. He takes three of the parts and lets the others divide one. And that’s where the term “The lion’s share” comes from.
Source: Why You Say It by Webb Garrison