It is up to the provider's clinical discretion to determine when the best time for their patient to test is. Please note, the CDC states,
Laboratory diagnosis of Lyme disease relies on a blood test that detects antibodies to the Lyme bacteria. It can take several weeks after infection for the immune system to make enough antibodies to be detected by the test.
CDC recommends the use of FDA-cleared antibody tests for laboratory diagnosis of Lyme disease. As with antibody tests for other infectious diseases, the accuracy of these tests depends upon how long you've been infected. Antibody tests may appear falsely negative during the first few weeks of infection, typically when a patient has an erythema migrans rash, but FDA-cleared assays have good sensitivity after 4-6 weeks have passed. Once your blood tests positive for antibodies, it will likely continue to do so for months to years, even when the bacteria are no longer present.