That lag is not turbo lag, it's BMW's craptastic e-throttle being terribly tuned. It's rediculous and is the number one thing I dislike about this engine. Press pedal, wait 1-1.5 seconds before the gas is actually engaged. You really do have to plan to hit the gas before you actually want to move. I even experimented with sitting at a stop light and tapping the gas repeatedly with no engine response whatsoever. Then I put it in neutral and park and it's nicely responsive. wtf is that?
I tried to get the dealer to do something about it in our X1 but of course "there is nothing wrong". Somehow I didn't pay enough attention to this before we bought. Thank goodness it's my wife's DD and not mine and she doesn't care.