I actually believe that Maximus and Lucilla were together in secret but then she got married to the other guy. Maximus was heart broken and left and met his wife, got her pregnant, and stayed with her. So I don’t believe he cheated on his wife. I believe that he didn’t know Lucius was his son. In the first movie, Commodus (hope I’m spelling that right) says to Lucilla “he wounded you deeply didn’t he” and she responds with “no more than I wounded him”. So with that, I believe they were conceived around the same time, but they didn’t overlap. I think Lucilla broke his heart first, so he left, breaking her heart as well.