No, that's not the issue. I think the issue is the animations they chose to use in the game.
To get an idea of what we are talking about, I want you do to something very simple with your character.
Stand still. Press space bar.
Did you notice that it took about a quarter second for you to leave the ground? It's not lag, it's because your character took time to bend his knees before jumping, thereby creating a delay between pressing the space bar and the actual jump occurring. That delay between pressing a hotkey and the action being carried out is what people are talking about.
This is not a frame rate or lag issue.