Hola Mahek
"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.
Saludos
Inma
