That's oversimplified, but you're absolutely right. His focus was that he got Reggie killed in the grand scale (although that stems from a completely messed up self-image and state of mind), and very much not about what he did to Xavier. Even before Reggie's death, it sounds like Lance was never as close to Xavier as the others, but whether he admits it or not, he didn't like being kicked out and abandoned by his crew/friends. Then he betrayed Cyrus who had really begun to trust him, so he's wallowing in negative feelings about the things he's done specifically to the people he cares about, not particularly including Xavier.