As rolli59 insinuated, "lag" describes performance issues caused by Network (i.e. internet) delays.
However, the GTX 260M (being a mobile GPU this performs lesser than a real GTX 260) should do okay for you. How well it does, depends on the resolution of the 22" monitor. Most of those are either 1680x1050 or 1920x1080. The lower resolution, the better the performance. The game you play, will also have a very direct affect on your overall performance. Not to mention the graphic settings within the game.
So your game will perform to a lesser standard (less FPS as rolli59 pointed out) on the external monitor, simply because there's more pixels to draw.