Makes you wonder a bit if there was a previous trauma that led to her being this way, or if she always was.
The spoilers contain information from Becca's side story, click at your own risk.
As for that, I have a hunch: I think her toxic personality is a product of her own mother's upbringing.
In Becca's side story, it's mentioned that Shannon was raised strictly by her mother. Interestingly, Shannon's father is never mentioned. Now this may have the following reasons:
Shannon's father left just as Trevor did years later.
It is pure coincidence and Shannon's parents were rather old-fashioned, in the sense that the wife stays at home and the husband works and earns the money.
Since Shannon already showed a rather unpleasant personality from her first narrated appearance when Jess turned up, it is strongly likely that this “me first and after me the deluge” personality was instilled in her by her parents. It's quite conceivable that her parents taught her this and they in turn learned it from their parents.
After she was then dumped by her parents to her aunt, Becca's great-aunt, I assume to keep the embarrassment of teenage pregnancy a secret and not to protect her from bad influences, her bad qualities were then probably reinforced by her aunt.
So if we assume that at least part of her family comes from a toxic home that they continue with their own children, then I also assume that Lilly would have been the prime candidate to become the next member of this toxic cycle if she didn't have Abby and Frank. After all, let's face it, yes, Frank is rather passive and they haven't had a good relationship for a long time, but Frank would have raised hell for Lilly too if Shannon had tried what happened to her.
And as for Becca's boyfriend:
after the events of the side story and the circumstances that her good friend knows about Becca's plans, I'm very convinced that all the stuff about her boyfriend is made up. She just won't have admitted it yet because she didn't want to admit too much of her plan and the boyfriend will just have been a buddy who helped keep Shannon away from her. I don't think it's far-fetched since we know Shannon was extremely jealous that Abby and Frank were close and up until that point everyone but Frank thought Abby was Frank's biological daughter. So I think it's quite conceivable that if Lilly hadn't had such a bad relationship with Frank and Becca hadn't had her “boyfriend”, she would have thought her own daughters were competition all the more.