@yldDavid the original chimera also lived in a cave deep in the mountains and goats are actually pretty good mountain climbers.
also the whole thing with the goat head doing magic comes from the fact that in the story of the chimera, the goat head was the head that was able to breathe fire.
( considering the head originally came out from the back/top side and not the front like the lion head, it was in no position to do anything else really )
basically it was a "normal" lion with a flamethrower goat head on its back and a snake head as a tail.