I love the suggestions of [name]Charlotte[/name] and [name]Elodie[/name]! [name]Lydia[/name] also comes to mind because of its Liddy nickname, but Loddie would be a stretch.
You could also give your daughter L.D. initials, calling her “Loddie.” For example, [name]Lucy[/name] [name]Diana[/name] or [name]Lorelei[/name] [name]Delphine[/name] (which actually gives you Lo and De, for Loddie).
I think that [name]Louisa[/name] was a great suggestion, too, especially with a D middle name.
Best wishes to you!