Depends on where you lunge and the purpose.
If you don't have an enclosed lunge Ring, then you need a lunge rein, 8-10m long. Otherwise you don't need it.
If you want to do more advanced stuff, like polework or use some kind of training aid, then you need a lunge rein.
You need a plain snaffle bit and bridle if using training aids. Something like an elyptical snaffle because it is double jointed and doesn't make a nutcracker action in your horse's mouth. Otherwise any other snaffle that you normally ride in.
Don't lunge in any other bit!
If you're wondering about training aids, best ask your trainer for advise but the most used ones are side reins because the horse understands them best. Ask your trainer how they should be used specifically for your horse.
It s probably a good idea to have a lunge whip because it helps for easier communication over that distance. Although it depends on how good your horse is.
I use the whip to direct my horses like to collect themselves or to turn around or to bend etc.
If you are free lunging for relationship and general excersise, then all you really need is an enclosed lunge ring😁
Best to get a really long whip, my loan charges when I just have a dressage whip so having one with more sound is better