Lutz,
The vehicle that we used was supplied by Lexus and was one of their Press Fleet. I cannot comment upon the wheel/tyre combination, but would assume that Lexus considered them appropriate as they knew what the event was. The tyres were checked prior to the testing so that pressures were not an issue. With that particular caravan (from memory and Abbey Spectrum?) the car performed well enough, and was fine up to the 60 mph test, but as my previous post suggests, at 60 there was a descernable sway, which was commented upon by at least one other of the judges.
Like you say, with your caravan, there's not a problem (which is great for you - after all, no-one would want to spend a small fortune on a car/caravan and then find it a problematic combination) and that may well be down to the weight differnce. All the car/caravan combinations that we used were ballasted so that the caravan was either 85% of the vehicle's kerbside weight, (or at the vehicle's towing limit if that was less than 85%), or to the 'vans maximum if the kerbside weight was in excess of the 85% (as per Land Rover Discovery etc).
Therefore, rather than wheel/tyre combinations being the critical thing, it might be that the Lexus is more suited to lighter caravans?