Hi OP.
I have very thick curly hair and got a terrible case of headlice when I was a child. We got rid of them by slathering my hair in a bottle of cheap conditioner, sectioning it and going through each section meticulously with a nit comb.
My hair was bra strap length and I wanted to keep it, but if I'd been a boy I think it would have been a good moment to have it cut shorter.
I don't think you need to subject your DS to a buzz cut but getting rid of some of the length would certainly help with the nit situation.
In your position I would try cutting it shorter so it curls around his scalp rather than shaving the whole lot off which might be traumatising for you both if his curly hair is part of his identity.
There are two things you need to get rid of: the lice themselves, and the eggs.
The lice are easy to spot, you know what to look for, they're horrible little creatures with legs. See them, comb them out. Keep going until you can't see any more, then keep going a bit longer.
The eggs are harder to spot because they are tiny and translucent and stick to the hair right at the roots. You need to scrape the nit comb hard against his scalp and make sure you're getting right in there at the roots where the eggs stick to the hair. Unfortunately, if you're doing it right, it should be a little bit painful and his scalp will be sore afterwards. It may actually be easier to scrape the eggs off the roots of his hair before cutting it, because you will have some length to hold onto, whereas if he only has a few inches of hair left it might be difficult to get enough purchase on the roots. It will also be much easier to section his hair if it still has some length to it, which means you can keep track of which sections you've already done.
I think I'd really go at his scalp first with the conditioner and the nit comb and try to get the eggs off the roots as much as possible. Then, if you want to cut it shorter, cut some of the length off at that point. If you're not handy with the hairdressing scissors you'll want to leave enough length for him to have a proper tidy up at the hairdresser's once all the nits have gone.
Do the conditioning and combing treatment once every other day for a good week or so until you're certain you've got them all, and keep checking his hair every day for the next few weeks.
Nits hate the smell of tea tree, so get him some nice pongy tea tree shampoo and conditioner to use going forward to discourage the little buggers from coming back.