Lee suffered his latest injury during the third quarter of his side's eventual 45-28 defeat to the Bears, although an MRI scan yesterday showed no structural damage to the neck, raising hopes that he could be fit in time for Sunday's match against the Green Bay Packers.
The 27-year-old was making his comeback in the match having missed the previous two games with a hamstring injury, keeping up his unwanted record of never having played a full 16-game season for the Cowboys.
"I hate being off the field. This happens way too much to me. But I am going to try to find a way to bounce back," Lee told reporters.
The Cowboys are in danger of not reaching the playoffs this season having dropped one win behind the Philadelphia Eagles in the NFC East with just three games left to play.