In a negative sentence, the word non must come before the object pronoun:

Non la mangiano. (They don’t eat it.)

Perché non li inviti? (Why don’t you invite them?)

It is possible (but not necessary) to omit singular direct-object pronouns in front of verbs that begin with a vowel or forms of avere that begin with an h. However, the plural forms li and le are never omitted:

M’ama, non m’ama. [Mi ama, non mi ama.] (He loves me, he loves me not.)

Il passaporto? Loro non l’hanno [lo hanno]. (The passport? They don’t have it.)