You can actually do the same deal on the line as in the round pen - to a large extent.
What you want to do is start a new program for your horse, starting with a new dialog for how you ask it to do what you want.
I re-train lunging starting by re-teaching leading. If your horse leads from your body alone (so the halter and rope are more or less an ornament... something you carry but don't "need") then it will learn to lunge much easier.
Once the horse is leading well and following my body language, I'll start paying out line and applying energy to the girth area (this tells my horse I want it to bend it's rib cage and begin a circle) and the flank, alternating as I need to create impulsion or fix bend to keep the horse moving in a circle. At this point I'm still going to walk "beside" my horse (so not just standing still in the middle), periodically I will take up a "leading" position again and ask the horse to be beside me... then ask them to move out ... and then begin asking them to stay out even while I stand in the center of their circle. I start at a walk and when we can manage the walk, with whoa... then I'll start on the trot.
Using this method I've found it takes minutes for the horse to understand the concept... and nobody gets "excited". I've used this for horses who are "lunge sour", confused, whip shy, or simply been allowed to goof off on the line (and therefore have learned to bolt, rear, buck etc. while on the line)... as well as for horses who have never lunged before in their life.