Lambert will be called up to start one of the games in Monday's doubleheader against Cleveland, James Fegan of The Athletic reports.
Lambert made two relief appearances for the White Sox in 2020, and he'll make his first major-league start Monday. He made five starts for Triple-A Charlotte to begin the season and posted a 7.71 ERA and 1.52 WHIP in 11.2 innings across five starts with the team.