Lucchesi was optioned to the Padres' alternate training site Thursday.
With rosters shrinking from 30 to 28 players Thursday, Lucchesi was one of the odd men out for San Diego. The left-hander struggled a bit in his two starts in the majors this season, allowing five earned runs on 11 hits in just 5.1 innings pitched. His demotion could signal the MLB debut of MacKenzie Gore; otherwise, Cal Quantrill could be an option to step into the rotation.