But he declined to address the details of current negotiations with Lawrence and his representative, David Canter, on a possible long-term contract extension for the free agent defensive end.
Lawrence played under the $17.1 million franchise tag last year and the Cowboys hope to get a deal done before the March 5 deadline before deciding on tagging him for a second straight year at a cost of $20.5 million and risking a holdout.
The window for putting the franchise tag on a player began on Tuesday.
Jones, speaking at a press conference for the upcoming IBF Welterweight title bout between Errol Spence and Mikey Garcia at AT&T Stadium, said the Cowboys are in the early stages of analyzing their roster and personnel.
He said the team plans to take a holistic approach of three years as they decide on deals for Lawrence and other obvious candidates for extensions like quarterback Dak Prescott, running back Ezekiel Elliott, receiver Amari Cooper and cornerback Byron Jones.
“We have many of our players we want to address their contracts in the future,” Jones said. “But the obvious ones are the obvious ones. And we got some work to do on others. We are still in formatting stage of how we are going to approach the overall picture.
“Not going to get into any specifics with any player, just to say the obvious is the obvious,” Jones added. “We’ve got a holistic thing we are looking into; holistic being this year or next year or even, if you will, even into the third year. In our case, we really need to make this a two or three seasons (thing). Not just DeMarcus, we are looking at our total player roster.”
The Cowboys have roughly $52 million in cap space available for 2019.
Jones also acknowledges that the team would look at the safety position in free agency. That means the holistic approach could include a play for free agent safety Earl Thomas.