Relief pitchers began to play a much bigger role in baseball in the 1960's. Up until then it was the hope and expectation for most starting pitchers to pitch complete games.
Ron Perranoski was a valuable contributor to the great 1960's Dodgers teams, and when he retired in 1973 after 13 seasons his 178 saves were the most ever by a lefthander.
Sparky Lyle broke that record with 238 saves over 16 years, with the Red Sox in the late 1960's and through the 1970's with the Yankees, and won the Cy Young Award in 1977.
Dave Righetti had some great years as a relief pitcher for the Yankees in the 1980s, and would have ranked higher in saves if hadn't spent his first few seasons as a starter.
Willie Hernandez was so dominant for the 1984 Detroit Tigers that he won the American League Cy Young Award and the Most Valuable Player Award.
Mitch Williams pitched 11 years in the majors from 1986 to 1997. His best years with the Philadelphia Phillies from 1991 to 1993. He finished his career with 192 saves.
#99 Gary Lavelle pitched 13 years and had 136 saves
#100 Jim Brewer pitched 17 years and had 133 saves
Other lefthanded relief pitchers that baseball fans might remember are...
Tug McGraw pitched for 19 years with the Phillies and Mets from 1965-1984.
Al Hrabosky had some great years for the Cardinals in the mid-1970's.
Mark Davis won the National League Cy Young Award with the Padres in 1989.
Eddie Guardado had some great years with the Twins from 2000-2005.
Jesse Orosco pitched in 1236 games (most in Major League History) from 1979-2003.
Mike Stanton pitched in 1178 games (2nd most) from 1989-2007.
It has always been and is still very rare for a team to use a lefthanded relief pitcher as their primary closer. Most teams use lefthanded relief pitchers as "specialists" or "set-up men" who pitch to one or two lefthanded batters before being replaced by a righthander.
The Best Lefthanded Batters and Lefthanded Pitchers in Baseball