Hi Clive.
It might be stating the obvious, but check your loading stratergy of the van. Have you got too much weight at the front and then put weight at the back to compensate. Loading the weight over the axle helps. Also the hitch weight should be about 75Kgs.
After that I'd get the load compensation valve checked on the suspension of your Lexus, this is supposed to dampen or stiffen the travel to suit road and load conditions.
You don't mention a stabiliser, I use a snake master (leaf spring type) on my Laguna for towing my twin axle van. while I don't require it as such as the unit is sway free, I do find it helps to control the yawing up and down. You see my van is inherantly too heavey at the front, and I have to put all the water canisters and waste canisters in the back bedroom of the van to get 75Kgs of hitch weight ( my car's tow bar weight limit). Being 24 years old, I guess Dean line were not too worried as they expected a landrover to be the tow car and they can carry a heck of a lot more on the rear.
Good luck and i hope you resolve the prob.
Steve.