The first two Lizzies I can think of were pretty much opposite characters - one quiet and good-natured, the other more outgoing and tough in character.
I don't think of Lizzie as dated or boring, because I haven't met many Lizzies (although I would think of Liz, Elizabeth and Catherine that way TBH). I like Beth (Bethany as full name?) and Liza, but not Libby/Betty/Eliza.
I really like the name Sophie (or even better, Sophia). I like Isobel (and Isabella) but it's really popular at the moment, if that bothers you?
Sophie Isobel would be a lovely name.