Lester joined the exclusive club in the top of the fourth inning when he struck out Arizona Diamondbacks pinch hitter Jack Reinheimer.
According to ESPN.com's Jesse Rogers, the only other active southpaws with 2,000 strikeouts are CC Sabathia, Cole Hamels and Clayton Kershaw.
It was an eventful evening for Lester, who also did some surprising damage at the plate.
Though the 33-year-old entered Tuesday as a lifetime .072 hitter, he connected on the first home run of his career, launching a two-run shot to left-center in the bottom of the third inning:
Lester finished 2-for-2 at the plate and struck out nine over four innings on the bump, allowing three earned runs on five hits and three walks.