Lawson was outrighted to Triple-A El Paso on Friday.
Lawson (elbow) was cleared to make his season debut for Double-A San Antonio last week and has thus far made two starts with the affiliate, giving up an earned run on three hits and a walk in 3.1 innings between the outings.
Lawson (elbow) was optioned to Double-A San Antonio on Wednesday.
Lawson (elbow) has been tossing bullpen sessions as he continues to recover from Tommy John surgery, AJ Cassavell of MLB.com reports.
Lawson (elbow) was added to the Padres' 40-man roster Friday.
Lawson underwent Tommy John surgery on Friday.