Was he treated & tested because of symptoms or “just” because you found a tick and maybe a rash?
What test has he had?
If it’s the standard test(s) then they’re looking for antibodies, not living bugs, and will show positive at least for a while even after a successfully treated infection. I’m not suggesting that everything’s fine as I’ve no idea of your lad’s history but don’t panic; wait for the advice of the docs. Do a bit of reading and ask some questions about how they know what they are telling you but he may well be OK.
I heard a talk a few years ago by a former head of the Lyme reference lab that was in Southampton – she had been part of a study that looked at antibodies in New Forest workers and residents and almost all the forestry workers (bar one, I think) were positive, as were a big %ge of residents. They were all symptom-free. If you get the appropriate treatment (and it sounds like he did) then I think you probably have to be unlucky to develop ongoing symptoms.
[Other opinions are available, conflicting and all over the internet. It’s a bloody confusing subject and I’m not pretending to be any sort of expert]