Pestano was sent to Triple-A Columbus on Wednesday, a day after he gave up a homer and allowed three runs in the ninth inning of a win over San Diego. Pestano has a 13.50 ERA in three appearances.
Pestano made Cleveland's opening-day roster following a rough 2013 season. He started last season as the club's primary setup man but went on the disabled list with a sore elbow in May and was demoted to the minors in July.
Pestano has had a noticeable loss of velocity.
Bauer will start the second game and be sent back to Columbus afterward.
Lee spent one day with the club last week when the Indians played a doubleheader in Oakland.