This isn't directly related, but I disagree with this. It is more engaging for the horse to be moved about when lunging. That way they have to follow you, focus on you in a slightly different place, and have an opportunity to go in straight lines. The key here is that you are the one deciding where to go, the horse shouldn't be dragging you around.
I do 2 types of lounging. 1) Exersize/training lounging 2) Lounging for respect (preride check)
For 1, I put the horse on a real lounge line, and like to stay in the same spot facing the horses barrel and keeping the pressure pointed behind their hindquarters. By relaitvely same spot, I mean a 3 foot radius from the center of the circle.
For 2, I just leave the horse on a lead rope and do more of what you are saying, I do much more moving with the circle when I do this. I lounge them in the same stance as lounge 1, but we only walk and trot, as to make sure the horse is calm, responsive, and focusing on me.
As she was doing training lounging, I said what I do for that type of lounging. I do agree with you about moving, I believe it is good to test and help a horse hone in on what he is doing and focus, but I don't like doing it on the long lounge line.