I don't know if the following refers to this Enoch Lewis or to his father Enoch. It comes from "History of the Episcopal Church in Narragansett, RI" p 515, posted on a family tree at ancestry.com and likely available elsewhere.
Littleneck Beach in South Kingstown was a one-mile race course for horses, notably the Narragansett Pacers, a prized RI breed now extinct. A silver tankard was the prize.
According to a story by I. P. Hazard, Enoch Lewis, a neighbor, said "he had been to Virginia as one of the riding boys, to return a similar visit of the Virginians to this section, in a contest of the turf; and that such visits were common with the racing sportsmen of Narragansett and Virginia, when he was a boy. Like the old English country gentlemen from whom they were descended, they were a horse-racing, fox-hunting, feasting generation."
According to Wikipedia, George Washington owned and raced a Narragansett Pacer.