I'm not so sure Rene sees the world in absolutes so much as she sees certain aspects of it in absolutes and others in opinions and assumptions she makes based on what she observes. By nature, Rene is suspicious of anyone who comes up out of the blue and talks to her. She's pretty dissociative, and has a habit of mistrusting people who approach her and that she doesn't approach first (since Lyon has made sure to teach her to be cautious of strangers). She's also not exactly the easiest person to get close to since she'll like you one minute, but then she'll dislike you or seem wary of you the next. Despite that, however, I can see her warming up to Danii eventually, but it most certainly would not happen immediately.
Unfortunately, this also counts for Danii being invited to their home. Rene prefers to be alone most of the time unless Lyon is with her, so it's really difficult to see her making such a statement unless she got really close to Danii (which is a situation I can't possibly see happening in backthread, though it might happen in game depending on how things play out). Lyon probably wouldn't do that either simply because he knows how Rene gets around new people. I can see a chance meeting between the three of them happening in the street, however.
As for the combatant angle, it'd have to happen without Rene and Danii would have to provoke Lyon somehow. She's lower class so she's not on his immediate hate list. She's also not a doctor. Otherwise, he'd probably just regard her or, in his case, probably not even pay very much attention to her unless she called out to him.
As for Dominic, it's really hard to say with him. He may or may not have had an encounter with her in the past. Unless she was attacked by thugs in the past or something, it's probably not likely though. In the event that she was, and Dominic knew of it, he'd certainly come to her rescue. Aside from that, there's pretty much just him knowing of her.
Florence is more plausible. A lot of Florence's meetings happen in that strange way. He sticks out like a sore thumb and, like I said, is extremely hard to overlook by token of just how odd he is, lol.
As for the crime syndicate, I don't know about that. XD Lyon would never, ever partner up with anyone. His cross is his to bear.