Lucy vs. Adelaide vs. Greta

None of them are bad choices. However, I think Lucy seems a bit nicknamey. I would use it as a nickname for Lucinda. Of your list, I think Adelaide is the sweetest. It's a place name with the option of a trendy nickname (Addie) or a quirky nickname (Delly). She has the option of blending in or standing out. Greta is really cute, but I would be concerned that she wouldn't have any options if she wants to be less unique.