The night before, Carlos Frias threw four scoreless innings. Those are the two primary candidates, with Ross Stripling getting a Tuesday audition that could move him into the conversation.
"He's got weapons, had a good camp, just get him over here in a big league game," said manager Dave Roberts. "Whether he's in the mix -- that remains to be seen."
Some will speculate that because Frias faced the Giants recently, Lee will get that first start, rather than have Frias face the same hitters again. San Francisco's lineup Friday night included Buster Posey, Hunter Pence and Brandon Crawford.
Lee, the Dodgers' No. 24 prospect, faced a White Sox lineup that included Jose Abreu, Austin Jackson and Melky Cabrera. He scattered eight hits without a walk or strikeout. He was generally satisfied with his outing, except for twice being unable to shut down the White Sox after his offense gave him a lead.
"Team gets a run, you want that next inning to lock it down and continue to add momentum on our side and I didn't do a great job of that," said Lee. "I elevated a little and they got some bloop hits."
Lee was sent to Minor League camp a week ago and told there weren't enough innings in Major League games to allow him to stretch out. But injuries have presented new opportunities.
"For me going into Spring Training I was always competing for a job and nothing changed when they sent me down," Lee said.
As the Dodgers did last year, there could be a revolving door for fifth starters. After using one in the fifth game of the season in San Francisco, an off-day will allow the club to skip the fifth starter the second time through the rotation.
In addition, management is keeping a close watch on 19-year-old phenom Julio Urias, whose innings limitations in past years leave his arm unprepared for a full Major League season.
After Brett Anderson's back surgery opened a spot in the rotation, Brandon Beachy and Mike Bolsinger positioned themselves as the two finalists, only for Beachy's repaired elbow to develop soreness and Bolsinger to strain an oblique.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.