Put your halter over on top of the bridle or lunge with just a halter and put your bridle on when you’re done lunging :)
I usually lunge in just a halter and it works fine
Think if I'm having to buy something I'll just get a cavession head collar instead of see if anyone has any at the yard. Thanks.
You can buy a little gadget that clips to either side of the bit (I know you have bit less but just to describe it) with a d ring in the middle for the lunge line to attach to. This might be worth you buyibg