In his Great Migration series, Anderson said that Richard Fairbanks arrived in New England in 1633, possibly on the ship, Griffin (per Savage). Anderson says that Richard's origins were unknown, and his wife Elizabeth's last name at birth is also unknown.
But.. There was a Richard Fairebanks in Boston, Lincolnshire, who married an Elizabeth Daulton there in 1618, and (possibly) this same Richard Fairbanks had quite a few children who were baptized there between 1618-1633. I was unable to find further children of Richard Fairbanks after 1633 in Lincolnshire. (see research notes in profile for sources)
The timing of Richard Fairbank's disappearance from Lincolnshire records (at least that I have found), coupled with Richard Fairbanks' migration to New England in 1633, makes me wonder if it is the same couple who came to New England...?