There always going to be some level of input lag for either a LCD monitor, LCD HDTV or Plasma TV. The only way to minimize input lag (at least after when the video signal leaves the graphics card) on a LCD HDTV is to put it "Game Mode" if there is such an option or to manually put to 60Hz mode which is he same thing.
When the HDTV is in 120Hz mode it basically does frame interpolation which doubles the numbers of frames received from the source. The primary use to make video play smoother for videos (such as movies) that are recorded at 24FPS instead of 30FPS. Basically in between every actual frame received from the source (60 frames per second) an interpolated frame is created which helps smooth out playback of videos with 24 FPS rates (like movies). This interpolation takes a tiny bit of time and it adds to the HDTV's input lag. Therefore all 120Hz and 240Hz LCD HDTVs should be switched to 60Hz mode when playing games.
Not sure about Plasma HDTVs since I don't really have an interest in them.
For absolutely no input lag after the video signal leaves the graphics card we need to go back to the old CRT "tube" TVs.