This Lilith has some unusual power to be overly aggressive and just gets away with it and even when Becca stands up to her, the guy/MC who is at the end of most of her abuse is nearly begging for her to stop. So much so they had to have the conversation twice. This is the same Lilith who basically accuses the MC constantly of being a creeper and would do things to women, while when they get back to the house after swimming she is upstairs groping the sister. The conversations and their outcomes border on the bizarre so far. Plot Armour at times is heavy. Lilith psycho ways might be toned down as she seems to be mellowing a bit towards the end. Maybe.
In case you forgot, or most likely overlooked it, Lilith was devastated when her dad (who she really loved) left. It left her devastated and heartbroken. This is why she acts like such a bitch sometimes, because she was really hurt. So she is protecting herself. But as you said, she is mellowing a bit, but that is because she is starting to realize that this Dad won't leave.
The oldest Daughter can even tell the MC is submissive and tells him so, it is why also no one really listens to him.
Yes she does, but she also tells him that he has a little dominance in him. Which is why the girls (Lilith and Abigail) are listening to the MC more and more.
But Rebecca, as the head chick (who recognizes the MC as the Alpha) is so cooperative with him, explaining the "pecking order" to him. And I think that Rebecca is the one who is most likely to melt the MC's resolve.
Edit: I hope I got the names right. I am a little drunk again. Yeh...a little. I think.