The Sky Bet League One club pulled off one of the biggest upsets of all time when coming back from two goals down against Chelsea at Stamford Bridge on Saturday to book their place in the fifth round with a remarkable 4-2 win.
Two years after becoming the first club from the basement division to reach Wembley in a major cup tournament - Bradford lost to Swansea in the Capital One Cup final - Phil Parkinson's side are at it again and Lawn said he was still trying to make sense of it all.
Lawn, whose wife Yvonne has been winning her own battle against bowel cancer, told Press Association Sport: "I want Man United for my wife, she's a big Man United fan, (co-chairman) Julian (Rhodes) wants them for the money and Phil wants them just from the playing point of view."
Bradford beat Championship side Millwall in a third-round replay and Lawn said the club's latest giant-killing run was worth around Â£700,000 in financial terms.
Bradford upset arch-rivals Leeds in the Capital One Cup earlier in the season and the two results have helped repay the club's Â£1million deficit in its overall playing budget.
"Phil pushes me and Julian very hard," Lawn said
"We've overspent nearly every season with him and have taken a risk - and he's repaid it to be honest.
"This year we gave him a million pounds more than we could afford (on playing budget), but he's repaid it.
"Julian and I aren't stupid, we know we haven't got that kind of money to put in.
"We were hoping Man United would sell Tom Cleverley and that the sell-on clause would help wipe out our deficit, but that's not happened yet.
"But Phil got us Leeds United in the Capital One Cup and we beat them, so we made in-roads with that, and now Chelsea.
"This current FA Cup run is worth Â£700,000 to us and so the two together have wiped out the deficit.
"So Phil can keep all his players now and look forward to building on the success we've had to make us even stronger."
Lawn ordered champagne to be sent to the dressing room at Stamford Bridge and joked he was now waiting anxiously for the bill.
"Has it all sunk in?," he added
"Well I still can't think of an upset in the FA Cup that's bigger than this.
"Two-nil down against the team who will become Premier League champions, among the favourites for the Champions League?
"To come back and score four goals? Let's face it, it's not as if any of those goals were scuffed or bouncing in off our arses
We played great football.
"When you consider how much the game has moved on, I think this is the biggest upset.
"In Ronnie Radford's day some of those Newcastle players were probably having a smoke at half-time
It's a different game now.
"Chelsea's second team cost them Â£98million against our's, which cost Â£7,500 and never mind the wages."
Source : PA