The White Sox reinstated Lambert (ankle) from the 15-day injured list Tuesday.
The 28-year-old righty made four rehab appearances with Triple-A Charlotte, surrendering five earned runs across 3.1 innings while striking out three and walking four. Lambert holds a 5.91 ERA and 1.73 WHIP through 21.1 frames this season, and he will replace Garrett Crochet (shoulder) in the bullpen after Crochet landed on the injured list Tuesday.