The way I see Lily she never abused or tormented the MC. She was (mildly) rude and sarcastic to him at times, yes. But that's not abuse. She never did anything to really hurt him and it wasn't malicious. It was defensive, a result of being scared to let him in and have him abandon her. And though it's been a while since I started playing and I may misremember, I don't believe it has been constant. She's a good person struggling with abandonment issues.
I can see how she fits the definition of tsundere, but I think she's a little more complex than the traditional tsundere; at least the way I've seen it portrayed and spoken about, where it is presented as very one-dimensional - they either have no reason to be antagonistic (it's entirely arbitrary,) or their reason is that they like the person and don't want to admit it.
None of this means you have to like her or, if you like her after she changes her attitude, want to fuck her. We all have different tastes and wouldn't it be boring if we didn't. Talking of boring. Meiko (is that her name, I can't care enough to be sure) is boring. As is the cliché story of the asian parents trying to marry off their daughter. If I can ignore one character, it will be her.
I do want to fuck Lily. But more than that I want to make her feel safe.