Lils
I'm gonna say this with the caveat that I haven't lived through having you lot yet and I don't know exactly why we named you as we did, but I do know that I'd never name a child after someone and expect them to be the same as that person.
Don't worry about what Lily's expectations are, you don't have anything to prove. As for the rest of it -- people only tend to remember the best of a person when they die, especially if it's a tragic death. I won't argue that they didn't do extraordinary things, they were both exceptionally bright, but it's not like your dad or I ever heard about any of the not-so-great moments from the people who knew them.