Perhaps Lothropp's principal claim to fame is that he was a strong proponent of the idea of the separation of church and state. This idea was considered heretical in England during his time, but eventually became the mainstream view of people in the United States of America, because of the efforts of Lothropp and others. Lothropp left an indelible mark on the culture of New England, and through that, upon the rest of the country.
Lothropp's advocacy for separating church and state significantly impacted both New England and American society at large, though his ideas were initially considered unorthodox in England.  His influence extended beyond just New England, shaping the broader cultural landscape of the United States.