I am publishing the answer you got in your support ticket, so that the community can benefit from it:
RadListView does not support drag and drop between two RadListView controls out of the box. However, you can refer to our Demo Application (DropDown & List -> List Control -> Drag&Drop example) for a demo on how to move items from one RadListControl to another. This example is for RadListControl but there is RadItemDragDropManager class that can be used with RadListView as well. This class provides drag & drop between two controls that have item collections. So, my advice is to try the approach from this demo.
All the best,
the Telerik team