Nope, no vibration what so ever. Its as vibration free as my old GX470, cant even tell if the car is on or not. I have the same GS350 AWD. Nature of the beast, lol, thats a good one. What beast? a Ford F350? Ask your dealer to start up another GS350 and let it warm up to normal rpm and compare the vibration.
I know there have been a few complains about 350 AWD with vibration problems, is your rpm normal? Some thinks its the engine mount, but to tell you the truth, I dont think the dealer or Lexus have a clue as to whats causing this. If the vibration is really bad, I would keep filing complains about the vibration to the dealer and to Lexus and try to get them to buy the car back. Just the other day, there was a 07 GS350 AWD on ebay with vibration problem selling at a very low price, I bet it was a dealer buy back.