I don't see why this belongs in Mental Health. Where I Live patients go to their GP's who then either decides to send people to a "regular" doctor for bloodtest and so forth, or establishes a possible mental condition and you are send to a psychiatrist/psychologist.
The brain is physical in nature, and lyme is far from the only disease to exhibit neurological symptoms. A psychiatrist will be biased towards treating as if the root is mental and not physical/viral in nature. Not to mention, they don't have direct access in many cases to do the required tests themselves.