Lawn, 52, has moved swiftly to head off speculation about the future of Parkinson, who guided the West Yorkshire club to a glorious Wembley double this season culminating in Saturday's League Two play-off final victory over Northampton, which sealed their first promotion in 14 years.
Parkinson, 45, has verbally agreed a new deal to keep him at Valley Parade, but will only put pen to paper when assistant Steve Parkin and fitness coach Nick Allamby have completed talks over their new contracts.
The Bantams returned to Wembley three months after their historic Capital One Cup final appearance and swept Northampton aside with goals from James Hanson, Rory McArdle and leading scorer Nahki Wells inside the first 28 minutes.
Delays over the management team's new contracts have fuelled rumours Parkinson could yet be lured away, but Lawn, who made his fortune after selling transport logistics business Driver Hire in 1999, dismissed the notion.
"Why would he consider that?" Lawn said. "We're in the black and well placed to keep moving forward. We're just waiting to make sure all three are happy with their offers.
"I think they're great contracts, but they want to sign them at the same time and I can't see it not happening. Next year we can have a good go at the play-offs. I think if we sit down and give Phil and his staff the right backing and keep that great crowd behind us, why not?
"In League One we think season ticket sales will improve and if we keep this momentum going, with our manager, we can have a good go.
"With more season tickets sales, (joint chairman) Julian (Rhodes) and I would put all the revenue back into the squad and Phil knows that.
"He knows what he's getting with us. Every penny that this club makes, he will get. It will be put back into the club to allow him to keep building."