Lindsey was drafted 37th overall by the Los Angeles Angels of Anaheim in the 2010 Major League Baseball Draft, out of Desert Mountain High School. Prior to the 2014 season, Baseball America rated Lindsey the 93rd best prospect in baseball. On July 19, 2014, Lindsey was traded to the San Diego Padres with José Rondón, R. J. Alvarez, and Elliot Morris in exchange for Huston Street and Trevor Gott.
On November 20, 2014, the Padres added Lindsey to their 40-man roster to protect him from the Rule 5 Draft.
Lindsey was designated for assignment on August 11, 2015.