If you do not have a cavesson, the USDF recommends that you attach the lunge line to the bride like so:
Step 1: Put the line through the bottom part of the inside bit ring.
Step 2 + 3: Put the line under the bottom of the bit ring and over again.
Step 4: Put the line through the top of the bottom part of the ring again.
Step 5: Continue under the horse's chin to the outside bit ring.
Step 6: Clip the lunge line to the outside bit ring.
*This prevents the line from tightening when pressure is applied. If the line is put over the horse's head, it creates a severe gag-like quality in the bit. If the bit is not looped around the inside bit loop or a Y attachment is used, the bit has a nutcracker-like action when pressure is applied.
A cavesson is the best choice, while using this method of attaching the lunge line to the bit is the second best option.