I try not to use Dawn. I usually clay after washing with Adam's Car Wash Shampoo and use the wash solution as lube. Detail Spray works well too. If I'm looking to strip the wax prior to claying, I'll drop about 2oz of Adam's All Purpose Cleaner in the wash solution before washing. The point of the APC is to remove as much of the wax, prior to claying, in order to reduce the amount of buildup in the clay. Your clay will work better and last longer if you strip the wax prior to claying.
If you clay properly, you will remove all contaminants, including wax. The point is to start with a clean slate.
Remember to use the baggie test when claying.