Lewis was also an anglicised version of Louis which was also a "so-called" English version of Ludwig.
One of my relations, Friedrich Ludwig Pfister called himself Louis Pfister in England, although he originated from Künzelsau in Germany and was Lutheran.
My own grandfather was called Christian Louis Pfisterer and was born in England. On being taken back to Kocherstetten in Baden-Württemberg in Germany, to be baptised, the name "Louis" was "crossed through" and he was baptised Christian Pfisterer.
"Louis" often replaced Ludwig and Lewis often replaced Louis regardless of religion.