I've gotten curious about this myth, when did it start, and who started it.
The earliest name dropped in this connection is Bishop William Meade (November 11, 1789 – March 14, 1862), third Episcopal Bishop of Virginia and enthusiastic amateur genealogist. He is *said to have* mentioned "Robert Lewis" as "an officer in the English Army" (there are no surviving records of any such person) and that he was "favorably mentioned in English history" (no such records). Whether Bishop Meade ever actually said any such thing requires further research, as the source for this information is of a far later date.
The first person to go on record with definitely garbled information was Captain Henry "Howard" (sic - actually Howell) Lewis (7 Feb 1817 - 17 Mar 1893), who claimed that "Robert Lewis and his wife, Elizabeth, sailed from Brecon, Wales on the Blessing, April 14, 1635" (mixture of truth and falsehood - the Blessing sailed from London, not Wales, in July 1635), and that "He located in what is now Gloucester, Va" (false - Robert and Elizabeth Lewis of the "Blessing" went to Massachusetts and settled in Salem). There follows a multiple smash-merge with Robert Lewis of *York* County and (of course) with the Lewises of Poropotank Creek.
And from there the myth grew and grew and grew....