Double lunging is a normal way of lunging your horse with addition of a second lunge line that goes around your horse's body on outside. This outside lunge line is like outside rein/leg at the same time. It can half-halt a horse, straighten deviating haunches and help to control direction with more precision.
When do I use double lunging? With a young horse after it becomes familiar with regular lunging procedure, accepts side-reins of comfortable length, accepts lunge lines/ropes around it's body and under it's tail. I also use it with older horses to retrain mistakes and badly executed movements like transitions or circles. In general terms, if I want a productive lunge line session I will do it with two lunge lines. I use one line only for a short warm up before a ride if applicable or to check horse's soundness.

Attaching and handling the lunge lines
The horse should wear a surcingle and a bridle. I attach the lines in a very particular way. The inside lunge line is run through the inside snaffle ring and is attached to the second top ring of the surcingle. The outside lunge line is attached to outside snaffle ring and runs through the bottom or second from the bottom ring on outside side of the surcingle. Outside lunge line goes around horse's body. This way of attachment provides additional control to the inside side including flexion, bend, focus and speed control. The top ring allows the inside lunge to work upward on the bit which facilitates the give and flexion and then reach forward and downward. Within 5 minutes of such lunging in trot a horse starts to stretch down, accepts contact and search for the bit, creating long and low frame. If my inside line was attached to bottom ring the horse's head would be pulled down more by force than aiding. A traditional way (to the ring only, or over the head) of attaching the line does not have enough precision of action.
The inside line is held in leading hand (left when lunging left and right when lunging right) and the outside lunge and the whip is held in other hand. It can feel overwhelming at first to handle all these lunge lines and a horse at the same time. Usually, I hold the rest of the inside lunge line in my non leading hand. This leaves me only with the rein like arrangement in my leading hand.
When you get enough practice and with a horse that knows the work you can take both lunge lines like reins in non leading hand (near hand), rest and the whip is in the other hand and run with your horse side by side. I love doing that, It feels so connected and clean. The whip I use for this work is either driving or in-hand whip. Normal lunging whip is OK too as long as it is rather short and light.

Working a Horse
If your horse feels fresh or a young one it is advisable to do 5-10 min single lunge line warm up before attaching the second lunge. Double lunging is as demanding on a horse as riding in terms of focus and obedience. If you lunge your horse prior to riding, you should single lunge him prior to double lunging. In double lunge a horse can be worked in walk, trot and canter. The changes of direction is impossible with the way I described the attachment of lines.
Walk - The horse should be encouraged to walk steady and with good rhythm, he is either on the bit or in case of a young horse contact with both reins. The exercises are straight lines (not always on the wall), circles of different sizes, corners, stretching with contact, halt, walking over polls/cavalletty, spirals.
Trot - Again as with walk the trot should be in control with good energy, connected or on the bit, swinging through the back, pushing off the hind legs. The beauty of double lunge is that unlike side-reins you feel your horse's mouth, you can change the frame, change the contact, encourage lightness, half-halt the horse, correct haunches that are swinging out, slow down on the aids, make transitions to walk or halt on the aids. All my horses are accustomed to move around the whole ring when being lunged. So, I do the same with double lunging. I end up exercising a great deal myself LOL. As described above when I take both lines in the near hand I simply run together with the horse. Exercises you can do straight lines, circles, lengthening and shortening of strides, transitions walk-trot, trot-halt-trot, spirals, long and low.
Canter - the great benefit of double lunging is schooling transitions to canter, trot-canter-trot transitions can be really improved with this method, things that can be fixed: wrong lead departures, rushing, head thrown up or out, pushing out, etc. Circles also can be done with good precision and of smaller size then riding allows at the moment. If you fit enough you can try lengthening the canter stride :). You can also use canter poles/cavalletty, particularly on a circle line.

Words of caution!

• This work requires you to be absolutely focused on the horse! Mind you any work with a horse requires that. Unfortunately, I often see people lunging their horse around them while they are chatting with someone, or even texting! This is will not earn your horse's attention and obedience!
• Moving with a horse requires a handler to be very aware of his/her position in space, body language, gestures, rhythm and posture
• There is a potential danger of you or your horse getting all tangled up in the lunge lines. If a horse gets tangled, let go of outside line and deal with your horse with single lunge line until he settles and can be stopped. Keep lunge lines neatly folded in your hands not in loops but in folds so they can be released quickly without "chocking" your hands. Do not let ends to drag, very easy to get your leg wrapped in it.

Being with your horse like that, seeing his reactions, exercising together not only improves both of your fitness levels, his balance and coordination but also builds better relationship as well.

Happy riding...