sentence - Superlative and definite article "the"

I have seen similar questions like this here on ELU. However, I am still confused with my particular question.

(a) She gets up latest in her family.
(b) She gets up the latest in her family.

Can one omit the definite article "the" in the second sentence?

There is a similar English Language & Usage question with an answer that says, “An article is only necessary in the superlative (or comparative) if the adjective is attributive (i.e. is in the same phrase as the noun it is describing)” .

Is the adjective in my above sentences attributive?