Genoa censu of 1820 shows a William Lewis as the only Lewis and had 3 sons that would be in the age group of Lemuel, its a good chance Lemuels father was this William Lewis
Lewis, William J. - Age, 18 years Enlisted, September 10, 1861, at Mexico; mustered in as private, Battery G, October 24, 1861, to serve three years; died of disease, January 14, 1863, at Camp California, Va --Take from NY Adjutant General Report 1896 1st and 2n Regiments NY Artillery