On my LG (42LW4500), game mode doesn't seem to reduce anything, aside from shutting off processing effects in a way that still doesn't reduce the lag. But that's probably a bug, as the setting does effect lag in newer models. One thing is that 42LW4500's processing is so fast that the games are still *playable* even when there's full processing.
What I do, on my LG, is to make sure I label the input as "PC", this is the ONLY thing that reduces the input lag for me. It goes on to disable further options but this time it does reduce the input lag.
One thing to note is, when you change to game mode, if the screen goes blank or there's stutter, it's more probable that your input lag reduction is working(as the lag changes, there HAS to be a sign when changing to that mode, on my LG it goes blank for a very short while when changing to PC label, some other sets may start displaying more recently input frames which may cause a slight jump in motion.)