I would have lost this bet.Xer Xian wrote: They do, and while no one has tested them for lag I'd bet they wouldn't score nicely.
Vincent Teoh of HDTVTest has measured the input lag of the mighty Sony BVM-X300 Master monitor (brochure here), and it's well under one frame. Apparently this monitor has very minimal picture processing (it does not upscale, it doesn't even deinterlace since it can render 1080i as is) which would explain the very good score.
Watch Vincent drool over this state-of-the-art monitor - I've joined him already