The sister is shitty, yeah, but she's also a victim in all of this. She has no right to let out her frustration on others, but also, I understand how much it must utterly suck to have no right about any aspects of your life, and to be treated more like some kind of object or trophy or something then as the person you are. When you try your hardest to get any affection from your family, and they thank you for it by trying to auction you off like some kind of lifestock.
It's not much of a justification, but in the end, she just did what her father taught her: venting out her frustrations by hurting someone she perceived to be below her.
And also, notably, we know that she played mean pranks on Lily before, but even Nekomori, who is by Lily's side at most times, has never seen her do anything of this level.
Once again, Lily deserves none of this, but I think it's weird anyway to bear this kind of animosity towards Suzu, who just told her dad - who she really just wants to appreciate her for once - that she was upset after a guy tried to rape her, and all he had to say in reply to that was "Well, you should have let him!".