I don't quite understand the conflict here. If the blind girl doesn't know what the brother likes she could just say anything. Just tell her your favorite foods.
The conflict is that Hana hates herself because she thinks she's the reason her brother died. Recall she was a second away from literally committing suicide in chapter 1 before Lily (inadvertently?) stopped her. She's not just doing this "become Kaoru" plan for Lily's sake, she's doing it as a form of suicide. By symbolically killing off "Hana" she can atone for her (self-perceived) sin by reviving "Kaoru." That's why she can't lie.
Anyway, I thought this chapter was good. It's not a perfect manga; it gets a little repetitive/slow in places and it leans too heavily on exposition sometimes, and Lily is a pretty flat character so far. I'm definitely curious to see where the current cliffhanger will lead, hopefully it won't just be a return to the status quo. I also am harboring a pet theory that Lily already knew or guessed Kaoru was dead from the beginning -- we already know he told her he was sick, after all -- and started treating Hana as him as a way to take revenge for Kaoru's death before genuinely coming to care for her as they interacted. It seems unlikely at this point but it would at least make her a much more interesting character.