Lee was given an offer she couldn't refuse..

Yeah, they keep making these characters go away for a while. Then come back all strange like this is the first time they are appearing on the show. lol

Yea I agree with your points, but..Gotham's handling of these characters is so weird. Barbara was a nice insecure girl, until ..she killed her family all on a sudden while tripping, went to an asylum and now a creepy woman. It's almost like writers didn't know what to do with her after the first season, and kept her anyway as she's integral to the Batman mythos. Kinda same goes for Lee, she went insecure and now entering a mob family..again, all on a sudden. That's some next level Batman Beyond crap. I was just staring at Ivy's arc, speechless.
How the name, "Martha" brought out the real Batman
http://i.makeagif.com/media/8-18-2016/8C46Hb.gif

Which Woman?
Barbara is likely the future mother of Batgirl and Jim Gordon Jr. She probably has to have them before she can take a dirt nap. Unleds Batgirl is named to honor her posthumously.
Lee is integral to Batman as her clinic in the area near crime alley is neutral ground in Gotham that even Joker honors. Lee fixes up criminals and vigilantes alike, and along with Alfred Pennyworth and Lucius Fox is one of Batman's few confidantes and friends. Lee won't be taking a dirt nap in the forseeable future. She can be sent abroad to get her off the show, but she won't be dying.
Presume that unless invented for the show (Fish Mooney) or merely implied to be someone (Jerome was made to lead us believe he was the future Joker), characters won't just die. Selina, Eddie, Penguin, Jervis, Harv, Hugo, Zsasz, Fries, even two of the Tweeds, all have plot immunity to Death unless they are meant to die (Crispus Allen) for specific plot related reasons.

I am so sick of this woman. She just needs to take a dirt nap.

The comic book version of Mario Falcone is actually based off Michael Corleone, so that is quite likely the case.

I totally got a
Godfather
vibe from that scene. Mario is Michael Corleone, not part of the family business, but will succumb and end up a villain.

Yeah, good point Pizza
It's going to be real interesting when Gordon finds out.

When she didn't know it's a mobster family she wanted to. Now she has to.
They were pretty rough, but they had something.
What was it?
I think it was the trousers.

I got the impression that she didn't know his family until Falcone showed up.
I didn't pick up any sense of surprise about the situation, and the details about raising his son apart from the criminal activity and not using the Falcone name seemed like Lee already knew the basics, but was just being given more details during the dinner.

I thought so too.
If it's all the same to you, I'll have that drink now.-Loki (Marvel's Avengers)

That WAS quick! Dude said "it's been less than a year" since she broke up with Gordon. Makes me think there was a set-up on his part.

I got the impression that she didn't know his family until Falcone showed up.
Yes. Plus, she's engaged to the guyalready?! That was quick!
If vampires hate "plus signs" - imagine how they feel about the "square root" symbol.

I got the impression that she didn't know his family until Falcone showed up.
I got new boots. Black, steel toe. Very dark, mature boots. All other boots are kiddie

Good for him! I'd put Lee at the bottom of that list, though, behind Vale, then Barbara.

Gordon has shagged all these women. Barbara, Lee and now Vale.

Which bimbo? Lee or Barbara?

There's no reason to bet; it's pretty obvious that's what's going to happen. Gordon and his boring bimbo reunite because they're doing the bumping uglies in real-life even though on the show they're boring together and have no chemistry. Yippee, dippy, the new casting couch.