All HDTVs, all of them, only accepts 60Hz input sources.
120Hz technology for HDTVs and PC monitors works differently. 120Hz (and 240Hz) HDTVs only accepts 60Hz inputs and does some video processing to improve smoothness and give video that "live" look.
Gaminng on a 120Hz or 240Hz HDTV will result in some input lag because it takes a little bit of time for the HDTV to do it's video processing before displaying it on the screen. It is always recommended to set the HDTV to 60Hz mode for gaming purposes to eliminate this induced input lag.