We have driven from Lexington to Baltimore and back in that time frame.
(starting out early in the morning and getting there in the evening hours).
But almost all of your time would be driving.
A lot of the college kids here like to use
Megabus, because it is so cheap.
It would save you money, but it looks like maybe NYC is the closest stop to you.
Its a ten hour trip so it wouldn't save a lot of time.
(My Son told me it was popular when he was in college. I am sure other people other than college kids use it though).
No Amtrack or passenger trains in Lexington. I think Maysville or Cincy has one.
You could rent a car from there, it would only be a short drive under 2 hours or so.