59cm sounds to big to me too unless she is still growing. I am 5'11" and my 57cm Litespeed is plenty big for me. You don't say which Litespeed it is, or if it is 9 or 10 speed but in my opinion it sounds like a very good deal for good components and a frame that will never rust, chip, fade, or wear out. I would have to disagree with the "great for a second bike" as it would be great for a first bike for most people. Whatever you end up with for her it is great that your daughter likes to ride with you.
EDIT: you posted while I was still typing. If you get it we want pics.