Lee held out Wednesday
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Cubs manager Lou Piniella said Lee will be back in the lineup on Thursday.
"If it were up to him, he'd play every day," Piniella said.
Lee, suffering from right thumb inflammation, was told to try not to do any type of baseball work pre- or post-game on Wednesday. The team's trainers wanted him to give the sore thumb time to recuperate.
Lee received a cortisone shot on Monday and said that he originally hurt the thumb diving for a ball in Monday's game.
Bruce Levine covers baseball for ESPNChicago.com.