Using "a lot" or "very much" to answer "how popular is something?" [closed]

No. Even accounting for answer ellipsis (see the Wikipedia article) (where you don’t feed back the understood parts of the question), the adjective popular would need a suitable adverb.

Q: How popular is he?

A: [He is] very [popular]. = Very.

Incorrect A: *[He is] a lot [popular]. = A lot.

Incorrect A: *[He is] very much [popular]. = Very much.