Phil Parkinson's League Two side will on Sunday become the first fourth-tier team to contest a League Cup final in more than half a century when they take on Michael Laudrup's Swans at Wembley.
But Lawn has revealed the west Yorkshire outfit may turn down the opportunity to compete in Europe next term if doing so would cost the club money.
Quoted in The Sun, he said: "I'm not going to pay to play in Europe. When we beat Villa (in the semi-final), I was told, 'You don't really want to get into Europe - it costs you money in the early rounds'."
He added: "I said, 'Well, that'll be fun because if it costs us money, we won't be there'. Realistically, it's not going to be a problem because I don't think we're going to win against Swansea.
"I won't put us in fiscal danger to play in Europe. That's not going to happen. I'm deadly serious. It's all very well saying there are financial rewards once you get to the group stage. But we're a fourth-division club."
Meanwhile, boss Phil Parkinson is determined the funds used from the Bantams stunning run to the final must be used wisely.
For a club who have teetered on the brink of extinction on more than one occasion since the big-spending days of 2000, when the likes of Stan Collymore and Benito Carbone arrived on fat contracts that could not be afforded, well over £1 million has been banked thanks to a staggering run to Wembley.
Victory against Swansea would complete possibly the greatest story in English football history. Even defeat can be accepted given Wigan, Arsenal and Aston Villa have been accounted for already.
What Parkinson would not accept, however, is the cash generated being frittered away. "The chairman has done a great job clearing the debts," he said.
"But now it is their job - and mine - to ensure this extra revenue is used to keep improving the structure of the club and make sure our supporters have a club that will flourish in years to come.
"As much as we want to enjoy this weekend, it is really important this revenue is used wisely. I am sure it will be."
- Sports & Recreation
- Phil Parkinson