Per wiki policy, Spoilers Off applies here and all spoilers are unmarked. You Have Been Warned.
Lucius is Maximus's son
We know Maximus and Lucilla had some affair in the past and she ended it. She ended it because she knew she was pregnant from Maximus and wanted to pass it as her husband's child. Maximus either knows this, or suspects. Since his recognized son is younger and he is very much Happily Married to another woman, the affair with Lucilla must have happened when Maximus was still single.Tigris of Gaul's mask was originally designed for Commodus
We know the film's production was a mess and that the script was rewritten several times. One of such rewrites was substituing Maximus fighting a rhinoceros for Tigris and his tigers when the film was well into shooting in Morocco. Tigris's mask looks like a man being eaten by a big cat... or a man wearing a big cat's skin, like Hercules. Who dressed as Hercules to fight in the Games in Real Life? Commodus. The idea is that Commodus would put in a Hercules-inspired suit of armor that included the Tigris mask for the final fight, but that this was abandoned when Tigris was written in and had to be made memorable. Joaquin Phoenix's talent convinced Scott to have Commodus unmasked at the final scene.Quintus takes over instead of handing power back to the Senate
Who's going to stop him? And his behavior has been ultimately self-interested.