Lawn accused TV chiefs on Thursday of "shooting themselves in the foot" after City missed out on a £247,500 live broadcast in the FA Cup fifth round.
City's home clash against either Sunderland or Fulham is one of only three ties that will not be shown live - a snub that Lawn branded "absolutely ridiculous."
Lawn seems to have a good case given that City's win at Chelsea was voted the FA Cup upset of all time by viewers on Match of the Day - but the TV companies have still decided not to bring the cameras to Valley Parade for the next round.
Joint-chairman Lawn blasted: "BBC and BT Sport have let themselves down with this. They've really shot themselves in the foot.
"We've scored the most goals of any club in the FA Cup this season, we've just pulled off the biggest shock in history and they don't come and get us. It's absolutely ridiculous.
"Who picks these games? West Brom v West Ham, is that really what the FA Cup is all about?
"I've had calls from everywhere since we beat Chelsea. Last night I was talking to Radio Ulster in Northern Ireland and Grant Holt was interviewing me for Radio Cumbria - everyone wants to know about what we've achieved.
"The whole world is looking at us at the moment and the TV broadcasters don't put us on. You've got to wonder if the people who decide these things actually know about football."
If, as is likley Cambridge United fail to win at Old Trafford, Bradford will in all liklelihood be the lowest ranked club left, with both Preston and Sheffield United ahead of the Bantams in League 1.
Had Bradford been drawn away from home and less likley to cause an upset you could see why the game was omitted from the live schedule but they are at home. On balance, the average viewer is going to be more interested in another potential Bradford upset than Premier League pairings like WBA against West Ham.
It's not as though the Premier League sides are short of TV revenue. On balance you have to say Lawn was right to have a go.
According to the FA, City's tie is scheduled for Saturday, February 14 at 3pm. But with Leeds hosting Millwall at the same time, that could be subject to change and the club are in discussions with police.
The games being shown on TV are: West Brom v West Ham, Crystal Palace v Liverpool or Bolton, Aston Villa v Leicester, Arsenal v Middlesbrough and Preston or Sheffield United v Cambridge or Manchester United.