Tu l'aimes plus que je ne l'aime.

English Translation

You love him more than I do.

Why there’s a “ne” in the end of this sentence? Couldn’t it be “Tu l’aimes plus que je l’aime.”?

I believe that this is the “ne explétif”.

Ne explétif - Lawless French Grammar

It mentions in the description that this is “formal and optional”, and lists “plus que” as a possible trigger in section 3 of the description.