Joseph Montoya would resign on April 9, 1957 after being elected to the United States House of Representatives (special election to fill vacancy for one of New Mexico's at-large seats). The office of Lieutenant Governor remained vacant for the rest of the term.
The source for the canvass is New Mexico Election Returns 1911-1969, compiled by the New Mexico Secretary of State in 1970 and available at the state library in Santa Fe.
Source for Popular Vote data: New Mexico Secretary of State, "For Lieutenant Governor," Canvass of Returns of General Election Held November 6, 1956 (Santa Fe, 1956)