I'd go after my lover. I would try to address the issues leading them to stray and try to heal our relationship, but it would hurt and it would take a long time to heal.
And if the person they cheated with was aware that my lover was taken, I'd raise hell for them, too. There is no excuse for that kind of disrespect. It says a lot about a person who is willing to be involved with someone else who is already in a relationship.
My father cheated on my mother with some chick at work before they divorced, and that woman knew he was married, he met my sister and I and hell, we even rode her horses, we went places with her. We thought she was a friend. Then we learned my dad was fucking her and I hated the woman. Hated my father, yes, but I wanted to salvage my relationship with him. With the bitch he cheated with, I wanted to torture her, punish her, make her pay for what she consented to. She helped him ruin our family. She knew the man was married and she knew he had kids and she pretended to be our friend, all the while fucking the man and giving him a place to run away to-- a place away from his real family. I hated her guts, and I let her know it at ten years of age. I continued to let her know it five years afterward, and when she decided she couldn't handle one of his daughters ignoring her and treating her like an inanimate object, she left him.
I'm still not sorry for it, either. 8D
Anyways. Back on track, if the person my lover cheated with wasn't aware of their relationship status, then I would have no grievance with them. I would make them aware of the situation, of course, but they wouldn't be at fault.