The roads themselves, with traffic enabled, will only run the traffic assigned to the region. This means you'll always have all the cars, lorries, and other vehicles on the roads. As always, there's a clever workaround for this. Some years ago, a clever Trainzer, I can't remember who, created Roadz. These are actually tracks and the other vehicles you run on these roads are really trains driven by AI drivers.
Look for lorries as type train and roads a type a track on the DLS. There are many, many to choose from.