you can do a CSF lyme test, but it is very painful, they will have to extract amniotic fluid from your spine, with a long needle, the operation is painful and a bit dangerous. I'd say easier is to send your blood to a lab that does more accurate lyme testing like IgeneX. If that turns out negative, you can rethink what u can do. As Girlie says, you have to have some antibodies to lyme in your blood, not always the case but it's worth a try.
"my lyme is primarily neurological" - what does it make you feel you have lyme ? u have the symptoms ? there are other diseases that can have some of them, it's very tricky.
if you have a lyme positive test and u have neuro symptoms, then i dont understand why u need to test your brain. you most certainly have it in your brain too ... i did not have any neuro symptoms when this started and as soon as i have taken minocycline, i had a terrible brain herx and then i found out i actually HAD neuro symptoms without knowing, i had some sort of fog on my mind that lifted, it was very subtle back then. Now it is very obvious, because it has returned