hi mate hope you sorted your problem
my ls400 does the same but over the spped of 70mph the whole steering vibrates
the problem front upper controls arm bushing or the ball joint of the arm.
you got two way of sorting it out
1:buy after market rubber and fit them in the upper control arm
2:if the ball joint got wear in it then you have to replace the whole arm.which is very expsive about £405 inc vat,