Lee, 29, missed all of last season with a knee injury. He has not been able to play a full season in his career, missing games with hamstring, toe, wrist, neck and knee injuries. He missed a series in last week's loss to the Atlanta Falcons in order to get eight stitches to close a cut on his lip.
Lee entered Sunday's game as the Cowboys' leading tackler, credited by the coaches with 34 tackles. He also had a sack, three tackles for loss, two quarterback pressures, an interception and two pass deflections.
The news didn't get any better for Dallas, as running back Lance Dunbar later left with a left knee injury on the opening kickoff of the second half. He was carted to the locker room and later ruled out. The Cowboys feared he tore the ACL and MCL in the knee, sources said.
Dunbar was to get an MRI on Monday morning. He was in a bulky brace after the game.
Dunbar was wrenched backward with his foot planted in the turf.
He will undergo an MRI on Monday once the team returns to its Valley Ranch headquarters.
"It doesn't sound good," owner and general manager Jerry Jones said. "They'll go back and do more technical evaluations of it, but I don't like the way it sounds."
Dunbar had three carries for 54 yards, including a 45-yard run in the first quarter.
A left knee injury also caused Dunbar to miss the final four games of the 2013 season.
Wide receiver Brice Butler also departed with a hamstring injury. He had one catch for 67 yards.
The Cowboys already were without quarterback Tony Romo (collarbone) and receiver Dez Bryant (foot), both of whom were injured earlier this season. Dallas also lost cornerback Orlando Scandrick for the season with a knee injury in training camp.