Why it's called lion dance when there is no lion in China?

At chinese legend,
Lion,dragon,tiger ,they all are believed to some noble beasts. especially, dragon is a kind of beast who is in charge of rainfall for emperor in heaven.Lion,tiger are guardians of immortals, Those immortals often ride a tiger or lion in old legend. Another Saying, lion is able to fight off ghost,monster.

the fact that lions extincted in China long long ago doesn't mean they never existed... the dance wasn't invented just yesterday...

The lion came from India and Persia...it went to China with Buddhism, and are believed to be protectors/guardians of the gods. That's why Chinese people put lion statutes in front of important buildings and have lion dance for happy occasions (ie. new years). It's for good luck and protection.