I love both a lot ❤️ The Lauras I’ve known have all been nice and successful, so I don’t have any negative associations.
Laura - strong, quietly mystical (with the word “aura”), and classic. Apparently Laura is close to the word for “penis” in Hindi, so that does worry me a bit, but it’s not an exact match
Also, I hope Laurie isn’t a possible nn! 
Lily - summery, lilting, and a modern vintage. The many spellings of Lily (Lilly, Lily-Mae, etc.) may be annoying, though.
My top list:
Laura
Julia
Charlotte
Lily
Anna (nn “Annie”)
My username is based off Dana Scully and I think Lily would be odd on her character, so it may not be the most adaptable name in the world
Still, it’s a happy name and Lily shows up in a lot of my fav books!