The White Sox placed Lambert (shoulder) on the 60-day injured list Thursday.
Lambert will get a second opinion on his injured right shoulder on Thursday in Los Angeles, Daryl Van Schouwen of the Chicago Sun-Times reports.
Lambert will be sidelined for 10-to-14 days after being diagnosed with right shoulder soreness Thursday, Scott Merkin of MLB.com reports.
Lambert (ankle) was transferred to the 60-day injured list Tuesday, Vinnie Duber of AllCHGO.com reports.
Lambert was placed on the 15-day injured list Monday with right ankle inflammation.
Lambert was removed from Sunday's game against the Tigers with right ankle soreness.
Lambert picked up the save Sunday against the Guardians, working around a hit in a scoreless inning.
Lambert was recalled from Triple-A Charlotte on Wednesday.
The White Sox recalled Lambert from Triple-A Charlotte to serve as the 27th man for Thursday's doubleheader with Toronto.
The White Sox optioned Lambert to Triple-A Charlotte on Thursday.