The Cowboys placed the franchise tag on the star defensive end for a second straight year, and the two parties have until July 15 to work out a long-term contract.
"(A contract is) in the works," Jones said on Monday, via the team's website. "We're communicating. That's what you've got until you actually meet to sign the contract."
If a new deal isn't reached and Lawrence signs his franchise tender, he'll play under a one-year contract worth roughly $20.5 million.
The 26-year-old is expected to become one of the NFL's highest-paid defensive players eventually. He's not taking that lightly, and neither is the team.
"This is a significant thing for not only our franchise but DeMarcus' life," Jones said. "It would make anyone be very, very judicious as they are working through the terms of this agreement. So the fact we don't have something done today is not inordinate when you look at the things that are at stake here."
Lawrence recorded 64 tackles, 10.5 sacks, and two forced fumbles during the 2018 campaign.