Lester is still slated to be Chicago's Opening Day starter against the St. Louis Cardinals on April 5.
In his last start, Lester gave up seven runs against the Padres.
"(It's) not pain," Maddon said on Friday, according to ESPN. "A lot of guys go through that moment where the arm just doesn't feel right. He came out of the chute really strong and probably went after it too hard, too early. Possibly trying to impress everybody, just being Jon Lester."
The pitcher signed a six-year, $155 million deal with the Cubs this offseason. Lester played the first eight-plus years of his career with the Red Sox before he was dealt to the A's in the middle of last season.
Lester finished 2014 with a 16-11 record and 2.46 ERA.
- Stanley Kay