Lexington and Livingston are both places near me, so I can’t see them as first names.
Leighton is okay though. I have met a little girl with this name and it doesn’t seem as much of a surname as the others. I would think
Leighton with this spelling would be a girl because of the
Leigh part, but I could see
Layton on a boy being pronounced the same. Livingston would definitely be a boy. I’m not sure on Lexington. Maybe unisex.