yes but it could be a bad video cable (see if any pins on ends are bent) or bad electronics in the LED monitor
don't assume it can only be the video card in the apple, because the LED has electronics in it that can be bad too. (video cards do have a splitting feature HOWEVER, that feature splits cleanly - you'd have a terribly damaged card to be displaying the wrong mode and have corrupted display too - as if overclocked - but you didn't overclock it)
try a different monitor
does your LG have PIP feature? (picture in picture?) if so, then that's another indication the monitor (or cabling) could be the issue. does your monitor have input signal choices? are the choices default?
is your apple clean? unplug it, blow dust out if any (open lid, if you see significant dust, clean) (be very careful not to "spin fan fast" and don't touch fan or anything metal) (or have apple store clean it if dirty). check the video connector on the outside of box. does it look like the pins are all clean and straight?