Lindsey played baseball at Hollywood Hills High School in Hollywood, Florida where he was teammates with Bob Fallon, who would also go on to play for the White Sox.
He was signed by the New York Yankees as an amateur free agent in 1981. Lindsey played his first professional season with their Rookie league Paintsville Yankees in 1981, and his last with the White Sox' Triple-A Vancouver Canadians in 1988.
On May 4, 1984, while playing for the Nashville Sounds, the Double-A affiliate of the Yankees, Lindsey caught a no-hitter by batterymate Jim Deshaies.

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