I'm not absolutely sure I ate at The Bistro, but I do remember specifically some years ago reading an article in The State or Free Times about a new pizza place and driving to Lexington to check it out. The restaurant definitely had an enclosed patio where I sat, so I'm thinking it was The Bistro.
In the event, I really didn't care for it. I felt that there was something to the pizza sauce that wasn't to my taste -- too sweet, if I recall correctly. (I feel the same way about The Pizza Joint).
The place is in a kind of an interesting little mini-mall with The Flight Deck restaurant which I may have to check out one day.
(Hat tip to commenter O'Reilly)
UPDATE 9 November 2011: Added Brix Bistro to the post title based on the comments, which led me to dig up this 2001 Free Times Review which is, I believe, the one which sent me over there in the first place.