The League wants to create four divisions of 20 teams below the Premier League in time for the 2019-20 season, increasing the number of professional clubs in England from 92 to 100, but Lawn is vehemently opposed to the plan.
"We've had this structure for years because it has suited the majority of clubs, so why change it?" Lawn told Press Association Sport.
"Why? What they don't understand is that currently we have 23 home games
We need the crowds
We don't get the money Championship clubs get.
"Losing four home games means we lose four incomes
It's not so bad for us but for teams like Accrington and York that's a lot of money
Lawn said he had not heard about the League's plans for a radical shake-up until advised by Press Association Sport.
"They certainly haven't come out and consulted with all the clubs because this is the first I've heard about it," he added.
"If we were voting now I'd be voting against it
The only reason I can think of is that, yet again, the Championship clubs want it."
Peterborough's director of football Barry Fry said his club had not been notified of the governing body's intentions either.
"I'm very surprised with all my contacts in the game that I didn't know about this already," he told Press Association Sport.
"Until I see the proposals and how it affects the clubs I can't really comment."
Source : PA