He opened it up to her and led her by the hand into it. He did this with a pure heart and not for any gain, save her friendship and affection. Not much to ask.
Yes, itis. A guy is not entitled to a romantic relationship with a girl he's friends with. It doesn't matter if he didn't have any ulterior motive in befriending her (and FYI? Befriending her in the hopes of getting into her pants is a huge ulterior motive). It's solely up to the girl to decide if she wants to reciprocate his interest, and if she doesn't, that doesn't make her a heartless bitch who just used him. Rather, it means that he failed to successfully use his friendship with her to get what he wanted from her.
If we're the Lily cult, what does that make them? "Cult" is too mild a word for the way they lionize Snape and bend over backwards to absolve him of every wrongdoing and place the blame on everyone who in their minds wronged him.
No one ever owes anyone friendship, even. For any reason at all. You don't have to be friends with someone you don't want to be friends with.
not for any gain, save
Go back to the start, do not pass go. "Not for any gain" means not for any gain. You can't say "not for any gain, except" and have it make any sense.
Fwiw, they're painting Snape a lot creepier than even I think he was. I really do think he just wanted to be friends with Lily in the beginning, and he wasn't thinking about objectifying and using her as Nice Guys do to the women they inflict themselves upon.