The 1998-2000 models you have a single igniter per spark plug. Everything is checked by the computer during running and it will detect misfire in each cylinder and store a fault code. Get somebody with an OBDII fault code reader to check. I would be very surprised if it was plugs, but if they are due for changing nothing wrong with forced maintenance.
On the earlier cars the engine, transmission and also the diff mounts could give trouble. Since you have changed the motor mounts and saw improvement, did the trans mount get done too? Won't be the diff though because you said it happens in park too. The fuel injection system has a cutout at the 1800 rpm mark, I wonder if its a fueling problem. Fault codes would report that too.
Hope you track it down....
Thanks, the transmission mounts are next. I forgot to mention that the LS had the 60k service done last time it was at Lexus....so that would cancel out the spark plugs. I appreciate all you guys have suggested.
Is it possible that the transmission could cause this when the motor is in park and you are running the motor at 1800-2200 rpm? Does the transmission turn at all to cause this vibration??