-My favorite animal is a lion? - Grammatically correct, but you would only use it to mean there is one specific lion who is your favorite animal. ex: My favorite animal is a Lion. He lives at the zoo and his name is Bob.
-My favorite animal is lions? - wrong, due to unmatched plural and singular.
-My favorite animal is the lion? - correct, and the most natural/common of the choices.
-My favorite animal are lions? - incorrect. Just add an S so animal, and it would be okay.