I've never had a lesson but my husband has. He took them from a now friend of ours who was a grade school teacher before going to horses full time. She is great with kids, wish I could ship her to you.
I know my husband spent so much time just walking around in circles he would come home dizzy (he was a beginner). I think we paid around $350 a month and he had his own horse. That's with him riding as much as he wanted. He spent about 1 hour every day with the trainer, but could stay and ride his horse longer if he wanted. That's been about 8 years ago so the prices have probably
My main point is, don't let your son get discouraged. The beginner lessons can get a bit boring for a young lad.
Also bless you for being a good parent and getting him some professional help rather them making the mistake so many parents make. Buy a horse, put child on horse, child falls off, child never gets on horse again
Or God forbid the child gets badly hurt.