You can to his office and interact with him, you max out when you get to the last scene.To keep Luxe alive, you need to either take his side or settle the conflict peacefully (requires 100 approval with both Luxe and Mirri). Mirri's approval is easy to gain - have sex with her (doesn't matter if dom or sub) repeatedly, kiss her and take her to the waterfall. To max Luxe's approval, be sympathetic when he tells his story and stay with him after dinner.