Team Logo. The Lynchburg Red Sox were a team in the Carolina League. They were the High-A affiliate of the Boston Red Sox. In 1995 they changed their name to the Lynchburg Hillcats. Retrieved from "https://prosportsteams.fandom.com/wiki/Lynchburg_Red_Sox?oldid=10008" Categories: Former CarL Teams Teams in Virginia Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.