I think either option will suck in the next episode. DPC never focuses on a non-main-LI character this much. I really doubt we'll see any meaningful development on Lily's end. If you didn't break the
contract, I think she'll be a little disappointed. But since she's not good with facing her feelings(she's good at ignoring them, not the same thing), she won't be able to embrace her disappointment and involuntarily end up avoiding you. And if you did break the contract, she'll have no idea what to do. At the end of that scene, she doesn't storm out. She runs away. No yelling, shouting, drama, swearing, not even a little remark. She just escapes. Because she doesn't know what to feel or do and I don't think she has ever been in this situation. Rather than facing it, this time she'll willingly avoid you.
So regardless of your actions in this episode, she'll avoid you most of the time in ep12–either to avoid drama or to avoid confrontation. But I still think at the end of the episode that will be some sort of reconciliation–just won't end in a scene that will take place in the Gallery, similar to Zoey's scenes in this episode. I believe this kind of storyline makes sense, it's a logical next step for Lily's progression and it allows DPC to focus on other characters. After ep12, I may be wrong. Maybe DPC will focus on Lily for the 6th episode on a row (I don't know if he ever did that for any other Others LI) and then I'll say the same thing for ep13

.