I have a split ear bridle on her with a snaffle bit, the halter is just under it.
This was the first time I'd done this with her, so please bear with my inexperience.
I did not want to get into all of this here as it is OT.. but you indicated inexperience and so here is more about lunging and it may help you and others (or not
Lunging a horse is more than driving the horse in a circle for exercise. You can teach a huge amount to a horse while lunging. First of all you need to either buy a lunge cavesson OR put a snaffle bridle on the horse and run the lunge line from your hand, thru the snaffle ring closest to you up behind the horses ears and then snap the lunge line to the ring on the side away from you. NEVER use a lunge line with a chain on the end. Use a lunge line that is 28-30 feet long (not the usual 24 foot ones you buy in the feed store).
This arrangement needs to be changed when the horse goes the other direction... and it is cumbersome. That is why anyone doing regular lunging of a horse gets a lunging cavesson with a ring in the center of the nose band. A cavesson will give greater and more sensitive control than the thru the bit arrangement.
Horses should always be lunged with side reins. If you use a saddle to lunge in instead of a surcingle, you attach the side reins around the girth straps, NOT to the horn (western) or the breast plate rings (English). Side reins are loose with the horse's head in normal position standing when you are first teaching a horse to lunge.
This is a proper equipment set up.
Next is your position. When the horse gets going, it is important to anchor yourself to a pivot point to help the horse know where the circle is. You only leave that pivot point to move closer to the horse or to get more behind the horse to drive him forward.. then return to the pivot point. As the horse becomes familiar with lunging and learns to track up on the circle, you should pivot around the heel of the foot that is toward the direction of travel (horse going clockwise, pivot on the heel of the right foot).
The object of lunging is to help the horse to learn how to bend and track properly on a circle at various gaits.. how to balance himself and use his hind quarters and to lift his front quarters. The object is to give him a reference frame to travel in and how to move into the bit. By staying anchored with the same (gentle) pressure on the line, the horse knows where to put each step and the circle is round.
When a horse is traveling propely on a lunge line, he is relaxed, balanced and willing. He transitions both up and down in an easy, balanced manner. the inside side rein is a bit loose and the outside rein is a bit tighter as he bends to the circle. He is on the bit and focused. The hind foot tracks where the front foot leaves the ground... hind quarters are neither inside nor outside the circle. The circle is evenly round. The horse works the same in both directions (clockwise and counterclockwise).
A lot of people toss a halter on a horse and lunge the horse. The horse runs around in a circle and that is all the horse does and really is not learning anything.
You can do this but lunging is a great training aid. Since our time with our horses is usually limited, why not take every last opportunity to use that time to help your horse train and be a better horse? Lunging can help a horse in so many ways when done properly... and it is an art when done right. Huge amounts can be learned by the horse and it is only about 15-20 minutes a day.