The Cowboys have three games in 12 days, starting Sunday against the Philadelphia Eagles, with a quick Thanksgiving turnaround against the Los Angeles Chargers. They play the Washington Redskins Nov. 30 at AT&T Stadium.
According to sources, the best hope is that Lee can return against Washington.
"It might be some time," coach Jason Garrett said Monday. "We'll see."
Lee suffered a hamstring strain in the first quarter of Sunday's 27-7 loss to the Atlanta Falcons and did not return. He missed two games earlier this season with a hamstring strain, with the Cowboys losing both games. The Cowboys have lost five straight games in which Lee did not play because of injury or was held out by the coaches as a precaution.
"Obviously when your front-line players go out you have to be able to continue to play and be effective," Garrett said. "Oftentimes that's seen on the offensive side of the ball, but it certainly applies to defense and certainly applies in Sean Lee's case. We simply have to play better when he's not in there.
"It's not only against the run, but it's against the pass. We'll continue to look at that, the personnel that we have in there, what we're asking them to do and just seeing if they're capable of doing it on a consistent basis. Again, we're evaluating that. We have to make sure we get better in that area."
The Cowboys are careful with players who have soft tissue injuries. Cornerback Chidobe Awuzie has missed six of the past seven games because of a recurring hamstring issue but is expected to practice fully this week.
Lee has missed seven games in his career due to a hamstring strain, dating back to his rookie year in 2010.
"You have to be very deliberate with this injury, obviously," Garrett said. "It's one of those injuries if you don't watch it, it can really go from being bad to worse quickly and you can lose a guy for an extended period of time. You want to make sure you handle it the right way as you would with any injury, but these soft tissue injuries can be damaging that way.
"We'll handle Sean's situation the way we always handle the injuries: If he's ready to play, he'll have a chance to play. We certainly will not rush him back. When he has an opportunity to play for us and help us, he'll be in the lineup."