on the ls400 you have bushings called radius rod bushings witch fail alot once bad the front end will shake there bolted on the frame with the radius rod going thru them the back of the rod connects to the lower control arm the front to the frame bushings r on the front
can you tell if the noise is coming from the front or rear or left or right side. Besides the shocks moving up and down the sway bar front and rear have sway bar links that may have failed but I suspect you would have been told this when someone was replacing the shocks. I have replaced suspension bushings in the front lower arms on higher mileage Ls 400s.
it sounds like its coming from the right side of car...and i had a back yard mechanic to put them on so i dont know whether he inspected anything other then struts...in the front.,.,.,.if you stay on smooth surface it hardly makes a sound...at slow speed you can really tell