My brother and SIL both have said that the Cadillac House downtown (SW corner of the main intersection downtown) has good BBQ ribs. I haven't tried the place myself, but I think I can take them at their word.
Edited for clarification: just talked to my brother and the ribs aren't what they used to be apparently. The last couple times they have had them they weren't as impressive as before. Still, there aren't many choices in Lexington...you may end up eating there anyway.