Parelli doesn't recommend lunging in circles. Lateral lunging, which is basically the groundwork for the Parelli levels, is what he suggests.
If you are lunging non-Parelli, you don't really need a cavesson. Some trainers swear by them, but I feel that the pressure they put on the nose, not to mention being lead with a lead on top of their head, is not natural. I have found that it is easier for a horse to understand what you want when lunging if you attach the line to the bridle. You can do this two ways: by tying a knot on the inside bit ring and fastening the snap to the outside bit ring, or you can pass the line through the inside bit ring, over the head, and fasten the snap to the outside ring. The latter is better suited to horses that tend to be more of a handful when lunging.