No, I don't like
Lulu as a nickname - too cutesy/frilly etc. I don't mind
Lula or just
Lu /
Lou.
I would use it as a nickname for
Tallulah or
Louisa /
Luisa.
Lucy and
Lou don't need nicknames (they are diminutives themselves), and
Lucy would be a more natural nn choice for
Lucia.
Luana is pretty, and I guess
Lulu could work.