The Lilith and Abby thing was established fairly early on, the theme first finding relevance when Frank and Abby visit Lilly at work to meet her boyfriend. Later it becomes even less subtle in Becca's debut where Abby and Becca talk while Frank is in the restroom and she more or less says that she's known about Abby and Lilly all these years. Narratively, it also makes sense to me that Frank is trying to set Abby and Lilly up: at this point in the plot, he's not ready to accept his feelings for Abby. Someone once told him, either Vanessa or Becca, that he either has to accept it or he has to live with her finding someone else. So for me it's only logical that he helps Lilly get together with Abby. Lilly is probably the only person in the story who loves Abby nearly as much as Frank does, he knows that she would never consciously do anything that would hurt Abby. So he has the advantage, from his point of view, that Abby might grow out of her crush on him, but he doesn't worry about her and still sees her as much as he does now, maybe less but not as much less as he would with a stranger.
And it also makes sense to establish Abby as an LI, I think. Lilly isn't exactly subtle about showing her feelings for Frank, even when Abby is around. Remember, in the beginning Lilly had a nip slip, Frank just points it out and she gets loud. A few weeks later, she undresses relatively casually in Frank's presence and cuddles up in bed with him. The only reasons I have that explain why Abby hasn't put 1+1 together yet will be that she lacks life experience and is probably rationalizing that Lilly is now overcompensating in this way for the last 10 years. Another theory is that although she has a suspicion, she doesn't voice it because she's worried that, at best, she'll embarrass herself again like in the first “Grabby Abby incident” shown or, at worst, Lilly will react so badly to it that she'll treat Frank the same way she has for the last 10 years.
Why it makes sense for Abby: As I said, Lilly isn't subtle, and sooner or later she's bound to do something Abby sees and confront them. I also think this is Becca's plan for Abby: Only by Abby showing initiative herself and telling them both “either you include me, or you can both forget about me” can Abby actively become part of this, and since Lilly and Frank don't want to lose Abby, they'll both have to comply.
As for Becca: she will definitely know by now whether Frank is her (biological) father or not. The preparations for this took place about 5 years before the current storyline and I can't imagine that a paternity test takes 5 years, even if you use carrier pigeons. And considering that Becca has hinted often enough that she would do the same with Lilly, I don't think she would mind if he was her biological father. That said, whether Frank is her father or a third unfortunate guy who ended up in Shannon's clutches, by the time Abby becomes LI, CNG will have to switch platforms with Single Again because Patreon would consider a sexual relationship between Frank and Abby to be incest.
Edit:
By the way, is it just me, or does anyone else think that Abby must have a cursed monkey's paw?
Abby wishes Lilly got along better with Frank: Lilly now cuddles up to Frank in Abby's presence while the three of them are in bed, and has no problem getting undressed in Frank's presence either.
Abby has always wished for biological (little?) siblings: her biological father turns up, who now has more children.
Frank really needs to teach Abby the saying “Be careful what you wish for, it might come true. Only different from what you think”.
