MAXIMUS: My name is Maximus Decimus Meridius, commander of the armies of the north, general of the Felix legions, loyal servant to the true emperor, Marcus Aurelius, father to a murdered son, husband to a murdered wife, and I will have my vengeance, in this life or the next.
This is the only time in the film that Maximus says his full name. It's also the first time his desire for revenge is fully articulated. Maximus' identity and his loyalty to Marcus Aurelius are very closely related to his desire for revenge, which is motivated by more than simply his family's death.
MAXIMUS: I have only one more life to take. Then it is done.
Maximus doesn't enjoy killing for its own sake. Everybody he's killed in the arena is just another step on the way to killing Commodus—"then it is done."
MAXIMUS: The time for honoring yourself will soon be at an end, highness.
This is definitely a threat from Maximus. These lines recast Maximus' earlier declaration ("I will have my vengeance"), and essentially say: "You'll soon be over Commodus, and my revenge will be complete."
COMMODUS: So, we will lie still and let our enemies come to us and nibble. Have every senator followed.
Commodus and Maximus are actually a lot alike. They both want revenge, and both are willing to "lie still" and wait. Revenge depends on careful, sophisticated plotting.
MAXIMUS: I will kill Commodus. The fate of Rome I leave to you.
Maximus' is bent on revenge, and in fact that's all he seems to care about when talking to Gracchus, as he is here. The "fate of Rome" matters much less to him than offing Commodus.