We have to confine our answer to the major league level.
Yes, in the majors, there have been left-handers who played second base, shortstop and third base.
Wee Willie Keelar, a Hall of Famer, played second base, third and shortstop 71 times over his 19-year career from 1892 through 1910.
Hal Chase, normally a first baseman, played 36 games at second base between 1905 and 1916.
Bill Hulen of the 1896 Phillies played 73 games at shortstop and two at second base in his only season with the club.
First baseman Don Mattingly of the Yankees played one game at second base in 1983 and three games at third base in J, 986 despite being left-handed.