The Guardians added Lively to their ALCS roster Tuesday.
Lively is not included on the Guardians' roster for the American League Division Series versus Detroit.
Lively (13-9) picked up the win Friday, allowing one run on three hits and a walk over five innings in a 5-1 victory over the Cardinals. He struck out two.
Lively (thigh) is listed as the starter for Sunday's game against the Rays.
Lively will start Tuesday's game against the White Sox, Joe Noga of The Cleveland Plain Dealer reports.
Lively (10-7) took the loss Wednesday against the Diamondbacks in the opening game of a doubleheader, allowing four runs on four hits and four walks over five innings. He struck out two.
Lively (8-6) took the loss against the Padres on Sunday, allowing two runs on six hits and two walks over 5.1 innings while striking out two.
Lively (7-4) took the loss against the Royals on Thursday, allowing two runs on six hits and one walk over six innings while striking out five.
Lively (6-3) took the loss Sunday against Toronto, yielding four earned runs on six hits and three walks in four innings. He struck out four.
Guardians manager Stephen Vogt said Tuesday that Lively (undisclosed) has checked out fine and is expected to make his next turn through the rotation, Mandy Bell of MLB.com reports.