Lovelady (elbow) threw a 20-pitch bullpen session before Tuesday's game versus the Yankees, Martin Gallegos of MLB.com reports.
Lovelady has been on the 15-day injured list with a strain in his left elbow since June 16. The left-hander will likely need to throw a couple more sessions and may need a rehab assignment before having a chance to rejoin the Oakland bullpen in the early portion of July.