Lawson is scheduled to work out with the Cowboys on Thursday, Todd Archer of ESPN.com reports.
The Cowboys are working out several pass rushers after Sam Williams sustained a season-ending torn ACL injury in his left knee during Sunday's practice session. Lawson played for the Jets in 2023, though he appeared in just six regular-season games while dealing with a back injury, and he finished the season with just five tackles (two solo). Lawson's most productive campaign came in 2022 with the Jets, when he recorded 33 tackles (18 solo), including 7.0 sacks, one forced fumble and one fumble recovery across 17 regular-season games.