RE: Lexington #1 Hours?
Other than I think they're closed on Sunday, let's assume the hours are something like 11:00 A. M. until 8:00 P. M. Monday through Saturday.
There are about 21 BBQ places in Lexington alone; several of the better ones are open on Sunday.
My advice is simple: either ask the police if you spot them, or grab a phone book and make a list. Then drive around a bit, leaving the car windows down (Lexington isn't crime central) and wait to smell the wood smoke. Several of the old-timers there use gas now, but more than not still cook in a pit.
Good luck, and let us know what you find.
As If On 'Cue, Ort. Carlton in Relatively Nearby Athens, Georgia.