All the tests Girlie mentioned would be good to get, but they will not rule out Lyme. Lyme can affect all those things, which is why they should be tested if you suspect Lyme.
IMO, ruling OUT Lyme is not reliable. Your doctor needs to look for clues that can help make a clinical diagnosis of long term Lyme and coinfections.
These should be done:
Lyme Western Blot showing all the bands
CD-57 (low CD-57 can be caused by Lyme)
Antibody tests for other tick-born diseases:
babesia, bartonella, ehrlichia, anaplasma, Rocky Mt. Spotted Fever
(any antibodies at all would indicate either a past exposure or chronic infection and should not be ignored but should be included as evidence of potential chronic infections)
Antibody tests for other bacteria and viruses commonly reactivated in those with Lyme:
mycoplasma pneumonia, chlamydia pneumonia, EBV, cytomegalovirus, various herpes viruses
(unusually high IGG titers as well as positive IGM titers indicates they are activating an immune response and are a drain on your immune system; be aware that symptoms of chronic infection may not be the same as acute infection; doctors tend to know little or nothing about chronic infections)