"A lot of young girls love that singer."
Translation:Beaucoup de jeunes filles aiment ce chanteur.
Beaucoup isn't a noun. It's subsequently incapable of being either singular or plural.
Even if it were a noun, the verb conjugates with the subject, which in this sentence is filles, so beaucoup still wouldn't affect the conjugation anyway.
EDIT: Okay, I'm not entirely sure what POS beaucoup is here - Wiktionary says it's an adverb, which it can be - e.g. Il pleut beaucoup en Angleterre - but that's not how it's used here; WordReference calls it either an adverb, a pronoun - e.g. Beaucoup l'a aimé - or a preposition in this case which seems wrong since it's not expressing a temporal or positional relationship. I think the best POS to assign to beaucoup de as a whole in this case is a phrasal adjective or something like that, but the point is, it's not a noun.
Okay, what you said is quite correct. beaucoup can be an adverb, a determiner or a pronoun.
The determiner is actually beaucoup de and act as an article, so the verb agrees with the noun of this article. Notice that in Beaucoup de filles aiment, filles is plural, so the verb is conjugated in plural, but if we say Beaucoup de pluie tombe, pluie is not plural, so the verb is in singular.
The pronoun is actually an abbreviated form of Beaucoup de X. Let's say we speak about children, and instead of repeating again and again beaucoup d'enfants, we just say beaucoup. In that case, it's always considered plural, no matter to what it refers, so we'll say Beaucoup aiment.