The Great Migration reference given is to a different John Lewis. This John Lewis does not appear in any of the Great Migration books.
The book which apparently identifies his ancestry is available on ancestry.com:
Moses, Grace McLean. The Welsh Lineage of John Lewis (1592-1657), Emigrant to Gloucester, Virginia. Baltimore, MD, USA: Genealogical Publishing Co., 2002.
It is difficult to flip through and find useful information. To remove the questionable tag you need to prove each generation until you hit a well documented and well-accepted line.