The League Two side would become the lowest-ranked English side to qualify for Europe should they beat their Premier League opponents at Wembley, but Lawn has revealed that the competition may prove too expensive.
Lawn told The Sun: "We would have to look at that situation if we were to win. Being a fourth division club, we can't afford to be going into Europe if it's going to cost us money.
"So we would have to sit down and take a close look at things should it come to that."
Bradford have beaten the likes of Wigan Athletic, Arsenal and Aston Villa in qualifying for Sunday's final.