*Membership spots not really limited!
She's working for Red. Has to. This is just another card Red can play when Lizzie needs another push away from her husband. Compromising photos?
Only problem with that idea is that it actively harms Lizzie. He might think it's best for her to kick him to the curb, but even if he's correct, it will still cause her great emotional pain and distress.
It would almost be easier on her for Red to simply have the man killed. Clearly, he could have his people make it look completely like an accident. She'd suffer some sadness, but would at least believe he hadn't betrayed her love. Her entire marriage wouldn't be shown to be a sham.
The man killed her father just to spare her the pain of learning the truth.
Thus far, Red has been fairly above-board in his interactions with Lizzie. He allows her to come to her own conclusions. And Red does hold to a code about certain things.