Try to play, paying attention to the END choice of chapter 12!
This whole comment is a big SPOILER, so if you care about it, please don't read!
Damn whore keeps pushing the conversation to the resolution that leads to "NTR", "HUMILIATION" and "DOMINATION", instead of "BOUNDRIES", "COMUNICATION" and "NTS"!
As for being in Lilly's corner, I have my doubts. Lilly is obviously excited about all the "dating Math" thing, about the new experiences, but she have doubts about the way things were going. She thought that things were going too far (and they were) with Math, to the point of the thing not being a couple play anymore, and go out of control. But she couldn't decide.
So, she passed the decision to the MC. He can choose to remain the experience with Math (which would lead to "NTR", "HUMILIATION" and "DOMINATION", acording to the red ! section), or finding someone new, who's not that much confortable with Lilly as Math is, which would lead to a more controlled experience, what is the original intention of the couple (being A PLAY, and not a domination situation).
Well, as you receive that message, damn bitch text MC, saying:" You know she wants Math". "Don't rob her of the thing she deserves"!
Man, the thing was going out of hand SINCE CHAPTER 10! To the point that the very Lilly felt something wrong, and she was the one benefitting from it! If she pushes to lead the situation to a point in which will become more, and maybe permanently, out of control, HOW CAN SHE BE CALLED A FRIEND?
And I bet she kept all these days filling Lilly's head with "go ahead, lose control"! In the same way as she kept pushing the MC to accept this NTS thing to start with! I bet Lilly accepted this thing because of her subtly pushing her during the days they spent together!
And this is the reason that I find questionable the thing about "being in Lilly's side". If she were on Lilly's side, she'd see the origins of the doubts of her friend, and consider the consequences that "play" can have in her life. After all, Math thing was only a play during a trip. Trip ended, she'd come back to her life, which's not with Math. Lilly didn't married Math, and she knew it.
But the whore friend had a selective burst of amnesia, apparently! She was more interested in seeing her friend fucking around and being a bitch like her, no matter the consequences, instead of keeping things as a healthy couple play the way it started.
You can see it clearly when she references "thing she deserves". In another words, "couple" was already card out of deck! What matter for her is what "she wants" and "she deserves"! This is why I said that she wanted to see things go to hell!
And, to put the cherry in this shit cake, if you choose to keep things under control, she curses you, calling you a "pussy"!
So, yes, Izzy IS NOT your friend! She DID things to undermine your relationship with Lilly, by insisting in a path that was obviously, evidently, going out of control, to the point even Lilly was feeling uneasy about! And that last comment of her makes crystal-clear what she really thinks about you and your relationship with Lilly!