Lewis is an English patronymic name from the given name Lowis, Lodowicus, and
comprised of the elements hlod = fame + wig = war. The founder of the Frankish dynasty bore this name, and it was popular throughout France during the Middle Ages before
being introduced into England by the conquoring Normans. When of Welsh extraction,
it is an Anglicized form of Llywelyn. The Scots version is a local place name for the
Hebridean island of Lewis, or as with the Irish, it is sometimes an Anglicized form of the Gaelic MacLughaidh , meaning "son of Lugaidh." Lugh was the Celtic god - 'Brightness.' Among the Jewish heritage, Lewis is a patronmymic form of Levi, or an Anglicized
version of a similar Jewish name.

Source:  Broken Arrow Publishing