With an English saddle ALWAYS run the stirrups up to lunge. I've seen people do it with the stirrups down and it bugs the heck out of me to see the horse slammed in the sides with the irons. I dropped a stirrup iron on my foot once... it HURT! Why slam the horse's sides like that repeatedly?? I can see where it might serve some desensitizing purpose, but I do something separate from lunging to make sure that the horse is not afraid of the stirrups. The most I would think of doing on the lunge is removing the irons and letting the leathers flap, and I've never felt a need to do that.... When I ride English, unless I'm in the saddle or hand walking some absurdly short distance and then getting back on, I run the stirrups up.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown