The Miller Challenge

The challenge is to find when George Miller (Müller) immigrated to the United States.
This is information about George:
He was born 5 July 1815 in Lembach, Bas-Rhin, France to George Müller and Sophie Catharina Guthöhrel. He was naturalized on 22 October 1851 in Lyons, Wayne County, New York. He belonged to the First Lutheran Church, where the records of his children’s births are recorded. His wife was Magdalena Rössel, born 15 December 1820, in Lembach. He first appears in the US census in 1850 as George Mills in Lyons. His oldest child, Magdalena was born 22 June 1843 in Lyons, so he must have immigrated before that. In the 1900 census, the first year the question was asked, Magdalena said she had immigrated in 1855, which is obviously incorrect.