Born in New Orleans, Louisiana, Lafont was a starting pitcher for the Tulane Green Wave baseball team from 1951 to 1953 and was a teammate of Ron Perranoski. The Dodgers signed him as an amateur free agent in 1953, and he made his MLB debut with them in 1955.
In 11 major league seasons, Lafont posted a 94–98 record with 1,131 strikeouts and a 3.75 earned run average (ERA) in 1,931 innings pitched. He pitched as a starter and a reliever, and was primarily a starter from 1955 to 1963, and mostly a reliever from 1964 to 1965. He was a two-time All-Star in 1959 and 1960, and pitched in the 1959 and 1963 World Series.
After his playing career, Lafont worked as a scout and pitching coach for several MLB teams. He also served as the head baseball coach at Lamar University from 1972 to 1981, compiling a record of 216–207. He died of cancer in Metairie, Louisiana, in 2011.