I'll age him up a bit so there's more of an age difference! so even though batman is technically a "hero" I totally see my guy kind of being villainous in a sense. so what she's involved in with definitely intrigue him and since he's so wealthy he might even put a hand in as well, we can figure it out in game! even though his reputation is playboy and money mogul, he's actually inanely smart so I can see them being attracted to each other because she always wants to be a step ahead and he's always 3 lol
as for their relationship, she's his arm candy that lasted longer than most expected. he usually has a new girl on his arm weekly (when he's not with his ex, above) and lil would have made multiple appearances. we can delve more into the workings of them and the timing but thats pretty much what I had in mind