At this point, a few facts about Shannon:
Bullied Abby's mother (for reasons unknown, but is there an excuse for this? Or rather the reasons were partially given, but why she continued to do it are unknown).
Tried to be a mother to Abby, but failed spectacularly as she became more and more like her mother visually and was quite a bitch to her
Also her dislike of Frank stems from the fact that he was married to Abby's mother and she thinks he is Abby's father. At this point I'd like to remind you that Abby only came along a few years AFTER Shannon broke up with Frank and consequently the wedding. And even if she can't know all the facts she should still be able to do the math.
was not really a good mother to Lilith either
Tried everything to screw Frank over in the divorce, including claiming he touched the girls
Now Lilith:
She's a daddy's kid, so she had trouble accepting Frank, hoping her biological father would come back
She has, and I think this was also addressed by Becca, rather bad taste in men and tends to make poor choices
She cares deeply about Abby and will do anything to protect her.
Her fling was mostly due to alcohol and unlike Shannon, she regretted it pretty quickly.
So, if anything, I would say that the only similarity Shannon and Lilith have is visual. Personality-wise, she's more like Abby's mother (cue male tastes). If at all one of her daughters resembles Shannon, it is Becca, in that they are both calculating and manipulative (let's face it, Becca is a good one but she is definitely manipulative).