Although no Churchill traveled on the Mayflower, the Fortune or the Anne to Plymouth Colony, Lemuel Churchill's mother, Lydia Harlow, was a direct descendant of two Mayflower Pilgrims.
For a look at the lines from Issac Allerton and Richard Warren to Lemuel Churchill, and therefore to his descendants, click on the links below. For more on Lemuel see both the link for Plymouth Colony and the one for Nova Scotia and New Brunswick.