Commenter Andy pointed out that this Internet cafe just to the right of Publix in the Lexington Place strip mall had closed.
I admit that that's far off my usual beat, and I wasn't even aware it existed, but he says
It was one of the few coffee/internet cafes here in Lexington, and it’s especially sad because it was local and always had a pleasant, relaxed vibe.
Judging from their still extant web site, they went beyond the standard Starbucks/Atlanta Bread/Panera wi-fi model in that they also provided on site printers and computers. I have found such places to be very helpful when I'm away from home and need to print out work documents, driving directions etc..
The name apparently came from the fact that there were three owners. I hope the association with "Three Bean Salad" (which I have always hated) didn't hurt them..
(Hat tip to commenter Andy)
UPDATE 3 April 2011 -- It's to be a yogurt shop:
(Hat tip to commenter Elisabeth A)