Lexington Grill in the Tenderloin?
Not ringing any bells. Also, no record of a food biz with that name in SF's restaurant inspection database. When I first saw your post, I wondered if you might have meant Lafayette Coffee Shop though its sign is not so exceptional.
I went there a couple months ago because I was craving Chicken Fried Steak. 2 observations: The couple who ran the place new 90% of the clientele by name and order (mostly old men). The chicken fried steak was home made. They took a piece of meat, pounded it and breaded it... as opposed to a frozen pre-made deal. This made for a tougher less "ground" consistency. No need to go back. If I was an older bachelor living in an SRO in the neighborhood I would eat there.