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 yesterday in a League Two play-off final victory over Northampton, which sealed their first promotion in 14 years.
The Bantams swept Northampton aside with goals from James Hanson, Rory McArdle and 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 dismissed the notion. He said: "Why would he consider that? We're in the black and well placed to keep moving forward."
Lawn added: "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."
Parkinson's side slipped out of the back door at Wembley after being handed a footballing lesson in the Capital One Cup final by Swansea, but that humbling experience played a crucial role in their marathon 64-game campaign.
Cobblers manager Aidy Boothroyd, born and bred in Bradford, admitted his players had suffered stage fright, while Bradford, comfortable in their surroundings, were quickly into the groove.
"It shows what sort of squad Phil and his staff have built," Lawn added. "They just haven't given up all season. When we lost 4-1 at Exeter back in March we were written off for promotion. I'd written us off.
"I told a waiter when we went for a meal on the way back that we'd blown it. I said Exeter would get into the play-offs and not us. But you don't write off this squad. It's down to their fighting spirit."