The Cubs are unsure if there was a definitive moment when he hurt that area of his shoulder.
Lake, hitting .304 with a home run this spring, played last year at Class-AA Tennessee and impressed his coaches in spring training, although he has a ways to go before making it to the major leagues.
"He's a pre-mediated swinger," manager Dale Sveum said on Wednesday. "There's still development there."
Lake was playing outfield and third base in camp. He is considered a possibility to be a long-term answer at third if he progresses.