With the $105 million deal inked, Lawrence is set to undergo surgery on Wednesday, NFL Network Insider Ian Rapoport previously reported.
The timeline of recovery following labrum surgery could put the start of the season in jeopardy for the Cowboys' most important defensive player.
"I can't put a timetable on how long it's going to take me to recover from the surgery, but I should be back before the beginning of the season," Lawrence told Eisen.
The 26-year-old then joked about missing preseason, intimating he'd likely skip those meaningless tilts out of precaution.
"The thing with this whole contract situation, and everybody wanting me to get my shoulder done, I think they keep forgetting that I played with a broken back two years in a row," Lawrence said. "I don't think the pain in the shoulder could ever match up to the pain I had to deal with with the back. So I don't really think (the shoulder) is going to be an issue. The only thing that could be an issue is if I try to rush it and hurt it again. Ain't no need to rush it."
(Sidebar: Latest reminder that NFL football players aren't normal mortals.)
Speaking on 103.3 FM on Monday, Cowboys EVP Stephen Jones confirmed the four-to-six-month rehab for Lawrence, who is already expected to miss training camp.
"Yes, you are always hopeful for the shorter time barring some complication," Jones said, via the Fort Worth Star-Telegram. "It was certainly a concern. He played with it last year. We felt like it in his best interest long-term. DeMarcus felt that way. We needed to get surgery. It turns out it got done in a timely fashion. We couldn't do a contract that wasn't good for DeMarcus and the Cowboys."