Defensive end Lawrence Edward "Tody Smith" is the younger brother of Charles “Bubba” Smith. Both played high school football for their dad, W.R. Smith, at Charlton-Pollard High School in Beaumont, Texas, where Tody was a prep All- American. 
 
Smith acquired his nickname in a junior high Spanish class. Apparently, “Tody” came from “Toro” (bull) because he was the largest boy in his class.
 
Smith attended Michigan State and Southern California. At USC, he was named All-American his junior year, 1969. He played only four games as a senior because of an ankle injury. Smith was one of the five African American starters that played against an all-white University of Alabama football team, winning 42–21 in Birmingham on September 12, 1970. This game was historically significant because it was a factor in convincing the University of Alabama and its fan base to accelerate its football team's integration.
 
A disappointing senior season was the only reason Smith remained available when Dallas drafted 25th in the first round at the 1971 selections. Smith was the Cowboy's No. 1 choice. He missed most of the 1971 training camp before signing and spent the first seven games of the season on the team's taxi squad. When he joined the 40-man roster, he quickly convinced the Dallas coaches he had a future in the NFL.
 
After the season, coach Tom Landry seemed convinced Smith could start in 1972. Although he had surgery during the off-season on an injured knee, Tody was ready to go in 1972 and was able to play in the Super Bowl that year.
 
He was traded to the Houston Oilers with wide receiver Billy Parks in 1973, in exchange for two draft choices. He stayed with the club until the 1976 season. Smith's final pro season was in 1976, playing for the Buffalo Bills.