"A lot" is functioning both as an Adjective and as an Adverb in the sentence.
Chocolate Cake does a lot.
Here " a lot" is modifying the the verb "does" and by definition, a word that modifies a verb is an adverb.
A lot of people.
Here "a lot" is modifying the noun "people". By definition a word that modifies a noun is an Adjective.