Spinal Fluid, Synovial Fluid and Synovial Tissue Tests
In spinal fluid the rate of getting a positive result from a Lyme patient is about 10% +/- overall according to some studies. In the Johns Hopkins lab test study (2005) that showed approximately 75% of people with Lyme disease are missed using standard blood tests, no spinal fluid samples tested positive.
As for testing knee or other joint tissues or fluid, there are many studies indicating the results are far from conclusive and many false-negatives will occur.
For example...
"Hold the Mayo" Clinic states... "We performed a retrospective review of 23,777 specimens tested by our Lyme real-time polymerase chain reaction assay to determine the percent positive rates by specimen source. The percent positive rates were highest in synovial fluid(6.4%) and tissue (6.5%), and lowest in blood (0.1%) and cerebrospinal fluid (0.09%). http://www.ncbi.nlm.nih.gov/pubmed/18947959
Harvard and Mass General studies indicate... "In patients with antibiotic-refractory arthritis, positive PCR results persisted for as long as 11 months, but positive results in samples taken during the postantibiotic period did not correlate with relapse or with the subsequent duration of arthritis, and at synovectomy, all results of PCR of synovial tissue were negative."
http://www.ncbi.nlm.nih.gov/pubmed/21590753
Even Yale, longtime promoters of unreliable tests for use in diagnosing Lyme disease, states ... "A total of 506 joint aspirations were analyzed. One hundred and fifteen aspirations were excluded. In the remaining group of 391 patients, 123 (31%) were subsequently diagnosed with Lyme arthritis. Fifty-one patients had culture-positive septic arthritis. ... For any child presenting with a joint effusion in a Lyme-endemic area of the Northeastern United States, the likely prevalence of Lyme arthritis is 31% overall and 45% in the presence of knee effusion."
http://www.ncbi.nlm.nih.gov/pubmed/21266639
Never exclude a diagnosis of Lyme disease based on results from any kind of lab tests.