Monty Roberts has a nice explanation of the bend issues and videos online of it. When asked to travel on a circle on a loose or lunged basis, the horse will instinctively put its nose and its bum to the wall, and tummy into the circle to balance. They "banana" in order to manage the task in hand. This develops tension in poll, neck, back and quarters and this is the wrong muscle development pattern. Additionally due to the way a lunge is often fastened the horse braces against the line.
Side reins offer the horse support laterally by providing a contact. The inside can be used marginally shorter to encourage the inside flex and thus the correct bend.
They also provide some contact for the horse to work into. Almost all horses will get faster when asked for impulsion, and will run faster, with a contact to work into that impulsion can be gathered up and thus engagement from behind begins.
Lastly, when riding we use the reins/legs to prevent the horse falling out through the shoulder, side reins provide a lateral support to help prevent this.
Lunge line is usually clipped to bit or through bit ring over poll to other bit. This is not a true mimic of rein contact and this addition of side reins provide that.
All that said, for me, best practice would be to lunge on two lines - as if long lining but stood to the inside. However it's tricky and unless very experienced, difficult to achieve a consistent contact
