Yes, this is actually very common. (
/sites.google.com/site/marylandlyme/tick-borne-diseases/epstein-barr-virus)
The Lyme keeps the immune system low, so that it can't fight off the viruses that we may have, so they have a tendency to flourish. You can take L-lysine (up to 8,000 mgs a day in divided doses) to help control the EBV virus and a couple of other herpes viruses.
umm.edu/health/medical/altmed/condition/herpes-simplex-virus