I've never had a round pen, though I have had a corral or two, the type one works cattle in for sorting and shipping. But, still, I've taught several to lunge just in their pasture or my yard.
Anyway, I start by leading the horse in a circle and gradually giving them more line while still encouraging forward movement with my arm. So, it may look like: if the horse is to circle to the left, the line is in my left hand and my right arm is extended outward toward the horse's hindquarters.
I rarely have to wave my arms to push them out and away from me. I don't use a lunge whip, mostly because I would probably fall over it!
But, I will add that two of my three kids can do it like I do. The third? She thinks we're all rotten because she has more trouble for some reason. I think it's body language and the fact that she gets distracted easily.