Hi, the problem I had was never fixed and never new what caused it, all I could do to make sure the car drove more stable is put suspension on Sport Mode. This was one of my main issues with the car, even skoda Octavia I had as a courtesy car was holding the road better.
I also had 4 new tyres (Good Year) fitted, wheel alignment was done couple times at Lexus Glasgow and it still was not stable - any move with your head and you already half the way to another lane!
I am sorry to hear there is another owner that suffers from the same problem! I wish I could get a shot in another GS to compare, that way I would spend money on suspension etc but mine was checked and all seemed fine, plus when I bought the car the mileage was only 33k miles so shouldn't be worn!
I hope you will find a cheap solution to it and soon. Otherwise the car was really good!
Good luck!