When I was growing up, a couple of my friends had
Lindsey sisters. They both claimed that in Scotland
Lindsay was used for boys and
Lindsey for girls. Since this all happened in South
Africa, I can't vouch for it! But I've always liked the name, regardless of -ay or -ey spelling, and I don't find it dated: it never really went viral here.
I don't associate it with lime trees, but since I was a kid I've had
Linden as a GP (fem).
I also knew a
Lynsey. She explained that her parents couldn't agree on her name: one wanted
Lesley and the other
Lynn. So they created a merger. One of her ex-boyfriends named his first daughter
Lynsey after her, because he liked the name so much.