I was going through Lanius' dialogue on the wiki since I decided to solve my problems with violence on my most recent playthrough and wanted to see all the other stuff he had to say. Based on my faint recollections of earlier playthroughs, he had the expected blend of arrogant boasting, conflation of honor and social Darwinism, and extremely non-PC threats to the player.
But I was not expecting how catty he is about Joshua Graham.
One of the ways you can talk him down is by conning him into thinking the NCR has set a clever trap for him like they did for Graham 4 years ago. It takes several speech checks to convince him, and during that convincing he says stuff like
"You dare speak that name? Comparing him to any man of Caesar will only earn you a slow death. You think me some lesser man, some other Legate? I am the first of the Legion, and this gate to the West shall be ours this day."
"Graham's overconfidence forever branded him with fire, I will not follow his trail of fire into the depths of the Grand Canyon."
Hoover Dam has never seen the massed strength of the East. Only Legates such as Graham… who deserved the fire Caesar blessed him with.
(side note: He sure doesn't mind speaking that name.)
He spells it out even more explicitly if you fail a speech check:
"I am not another Legate, and I am not such a fool as Graham, to be painted in pitch and set aflame."
That attitude isn't just arbitrary trash-talk. It's a defense mechanism. Lanius knows dam well (huehue) that if he screws up this assault, he's going down the Grand Canyon next. Everyone in the Legion probably thinks like this. Everyone from the must brutally cunning Centurion to the mediocrest recruit who saw that execution learned one clear lesson: If not even Caesar's bestie and co-founder is spared his wrath upon failing him, you sure won't be.
It's such a well-known attitude that Ulysses outright tells us "oh yeah you can totally make him back down if you bring up Graham and make him afraid he'll fail".
That's why Lanius reassures himself that he's built different. He's a greater man. He's not overconfident or a fool. He doesn't deserve to be executed. He's way cooler and stronger and more competent than Joshua Graham and he definitely won't fail and get brutally publicly executed, no sirree. Retreating from the Dam after assaulting it is a sound tactical judgment and 100% different from failing to take the Dam.
Tragically, we never get to see how correct he is in that assertion. Which is a shame because I would love to hear Caesar chew him out for withdrawing all of his forces after attacking the Dam just because of one persuasive postal worker.