The RX is known for this lag and most say it is due to the transmission which may be true. However, I eliminated the problem on my car by removing the slack in the throttle cable which connects the gas pedal to the throttle body. It is a very simple thing to do. I was concerned about taking out the slack because I assumed Toyota put it there for a reason. However, I did the adjustment a couple years ago and haven't had any problems. It made a huge difference!
Did you do that by yourself or a repair shop? I am still not very clear for the "slack" you are talking about. If you could up some pics that would be awesome.