Does it have dynamic contrast? Edge sharpening? Truecolor? any kind of "Better Picture" option??
those are called post-processing effects. Most 1080p tvs have these filters/effects. They can be great for watching TV or movies, but can cause a delay in what they recieve, and what they display.
Hence the Lag. Some Tvs are better than others.
What TV do you have?? make/model. maybe it does has an option that might be causing your issue. Maybe it doesn't.
So is mine, and most others that have "game mode"