To make room for Boscan on the 40-man roster, the Pirates also transferred right-hander Brandon Cumpton to the 60-day disabled list before Saturday's game at the Cubs.
Pittsburgh used seven relievers in Friday's 11-10 loss to Chicago. Boscan, 25, went 2-1 with a 2.87 ERA in six starts with Indianapolis. His previous appearance was last Sunday.
Boscan has never pitched in the majors.
Lombardozzi made six appearances with Pittsburgh, going 0 for 4 with a walk and a run scored.