Lawson recorded 2.0 sacks in Sunday's loss to the Falcons.
The Cowboys signed Lawson on Monday.
Lawson is scheduled to work out with the Cowboys on Thursday, Todd Archer of ESPN.com reports.
Lawson (coach's decision) is out Sunday against the Broncos, Randy Lange of the Jets' official site reports.
Lawson (back) wasn't listed on the Jets' injury report Thursday ahead of their Week 1 game versus Buffalo, Rich Cimini of ESPN.com reports.
Lawson (back) returned to practice Tuesday, Al Iannazzone of Newsday reports.
Lawson (back) may not be ready to suit up in Week 1 according to head coach Robert Saleh, Zack Rosenblatt of The Athletic reports.
Head coach Robert Saleh is hopeful that Larson (back) will return to practice next week, Skyler Carlin of USA Today reports.
Lawson restructured his contract with the Jets on Thursday, Field Yates of ESPN reports.
Lawson (ankle) was a full participant during the Jets' practice Thursday, Rob Demovsky of ESPN.com reports.