May lyme disease re occur?

Yes: Lyme disease may recur in 2 ways. It can be very difficult to fully eliminate, so even if someone has been successfully treated, the borrelia bacteria that cause lyme may be in the dormant cyst stage and may reactivate if the patient undergoes physical or emotional stress. Even if borrelia has been eradicated, being exposed to the bacteria again via insect bite etc. Can result in recurrence.

Yes: One can be reinfected.