Lumbar punctures and blood testing for these diseases are not a very good way to determine if one has them. These tests are faulty to begin with - looking for antibodies that may or may not be there. Not to mention that these bacteria can actually change their surface proteins, rendering the tests - and our immune system - mostly useless, since neither can detect the Lyme bacteria at that point.
I am in no way trying to convince you that you have a Lyme infection. only that you should be careful to not dismiss it too quickly. As you can see in this paper, Cerebrial Vasulitis can be from a Lyme infection:
brain.oxfordjournals.org/content/119/6/2143.full.pdf"We conclude that cerebral lymphocytic vasculitis and multifocal encephalitis may be associated with B.burgdorferi
infection." And Lyme is frequently misdiagnosed as vasculitis:
lymebook.com/blog/testing-diagnosis/misdiagnosed-diagnosis-mimics-great-imitator/