The issue here is not that your horse is strong, rather it is that your horse has not properly been taught how to correctly respond to pressure.
'Strong' horses are horses who, when pressure is applied to them, pull back and fight this pressure rather than give to it. I don't use a cavesson or anything fancy to lunge my pony. I use a simple rope halter and I can use this because my pony understands how to give to pressure. She used to be incredibly strong often tearing the lunge line from my hand, but with correct and consistent training involving the concept of pressure and release, I can lift the lunge line slightly and she will respond.
I do not support lunging horses with a bit. Not only does it promote habits such as leaning on the bit but it can desensitize them to the pressure in their mouth, meaning they can become 'dull' to the reins. Furthermore, if anything were to happen, such as the horse tripping up or getting caught in the lunge line, it will catch itself in the mouth, resulting in pain and most likely an injury. If you can, please lunge with a halter/headcollar.
Flexing your horse and making sure they give to the slightest bit of pressure is a great way to set you both up for success not only when lunging but riding too...
Begin by standing at your horse's shoulder, just slightly behind if you can. Run your hand down the line and pick it up, slowly bringing it towards you. If you're pulling and your horse is not giving you his head, bump the line and increase the pressure until he does. As soon as he gives you his head, drop the line and stop pulling. This is telling your horse that giving to pressure is the right answer and that resisting the pressure is the wrong answer. Repeat this until you no longer have to bump or pull hard with the lunge line. When you pick up that line, your horse should feel the slightest pressure and give you his head. When this happens, you've achieved getting a 'soft' horse. It takes consistency and your timing is crucial. This way really helped me with my own mare and I guarantee it will help you with your own!
If you have any questions please don't hesitate to pop over a message. I'm more than happy to clarify anything I've mentioned that you're uncertain of.
If your horse is strong something you can do that I have found really effective is to move your body more towards you horses bum. Think of using your body to push her bum out - this will keep her bent towards the inside of the circle and should keep her from leaning on the lunge line.
Half halt a lot!!! Just give and take on the rains until he is soft in his mouth! If He “takes the bit” and runs you Can just stop him until He soften.
So just be patient and do those tings. You Can always look up videos about The methods