I pretty much agree with you, but I don't think
Haven is awful. It has a nice meaning and isn't spelled weirdly. And since your sister's friend isn't family, then I don't see much of an issue with Aven and
Haven being similar (btw, I prefer
Haven). The two names will probably get mixed up for you and your sister, but that's about it.
Lily and
Haven are kind of cute together. Yes, they're different but not too bad.
"Nobody cares how much you know until they know how much you care."
Theodore Roosevelt