Working a horse on the double lunge is for a young horse an introduction to the reins for later riding or driving and another way to train every other horse. You have the same options with the double lunge as with the single lunge and still can lunge different figures. The benefit of the double lunge is the possibility to frame the horse between two reins what helps it bending and keeping track with its haunches.
It is also a step towards the work on long reins.
Next: Work in Hand