Lawrence is questionable for Dallas' game against the Jacksonville Jaguars on Sunday as a result of the injury. He aggravated the shoulder hitting Houston Texans quarterback Deshaun Watson early in the Cowboys' 19-16 loss last week.
"This is the first time it popped out on me last week," Lawrence said. "I was about to cry on the sidelines if y'all didn't notice. It was hurting bad. It feels better now.
"I'll work through it just like every other injury. It's very frustrating. If I'm out there, that's my whole purpose and I'm determined to get after the quarterback and I don't feel like I did that to the best of my ability."
Despite the injury, Lawrence played in every game last season, totaling a career-high 14.5 sacks and earning his first Pro Bowl selection. He has played in all five games this season and has 5.5 sacks.
Lawrence, who is practicing with a shoulder harness, said he could have surgery in the offseason to repair the labrum tear.
"Strap it up and see how it feels before the game, if it's not able to go, I won't go," Lawrence said, "but if I'm able to go I'll be out there. It's holding up for the most part."
Lawrence, 26, is making $17.1 million this season playing under the franchise tag. He said he isn't worried about the injury having an effect on his next contract.
"I do want my contract taken care of, but I don't feel like this is a major injury that's going to hold me back from getting my contract," he said. "Really, at the end of the day, how things are going, I keep putting up my numbers and they ain't got no choice but to make moves. We're just going to let that play out."
--Field Level Media