There are others here who know much more about the test results than I do, but I think some.times treatment causes the test results to go up temporarily, because the bugs are getting blasted into bits. I wouldn't assume it's a bad thing till you hear from the LLMD.
I don't know that LLMDs do spinal taps much, because it doesn't show anything that can't be known by blood tests.
How is your son feeling?
Spinal taps are often negative even if lyme is present. From what I have read few lyme doctors order them. I had a spinal tap done to rule out other things. Not to look for lyme.
Ditto to patsy10. Lumbar punctures are often diagnostic, not therapeutic. If you know he has Lyme, there is no cause of an LP. Like patsy, I had one to rule out other things. They did test for Lyme, but it came back negative and I've read that it is not a very good way to test for Lyme.
I too have read that WB results can become MORE positive early in treatment since the antibiotics get the immune system working. Remember, the test detects the Lyme bacteria indirectly through antibodies. So a positive test shows that the body is fighting the infection. Take it as a good sign that his immune system is pumping.
What type of doc is the Lyme doctor? If he is ILADS affiliated/educated then he should know a lot about treatment needs for persistent cases.