The rear of the car totally gives out, i.e. loud thump, and the rear wheels lose traction when going over a bump. The trac light comes up as well. Back suspension feels very stiff.
I thought it could've been the air suspension, so I had the the rear air struts replaced. No use. same situation.
what might it be ? any ideas ? thanks !

 

Take it to a mechanic. The LS400 has a 4-wheel independent suspension, with too many components to pinpoint the cause over the internet. If it's as bad as you say it is it should be apparent to whomever looks at the car.