"a lot" in this sentence is an adverb, not an adjective, therefore it needs "mucho" (not agreeing with any noun at all).
It would have been different if we had said for example:
I like lots of terror films.
This would then be "a lot of [something]/lots of [something]", as an adjective modifying "films". So in this case we would have said:
Me gustan muchas películas de terror.
I hope this clarified it.