Cotterill came into Fratton Park under extreme pressure to steady things after a turbulent season in the Premier League and Lawrence is hoping that Convers Sports Initiatives hand the former Stoke City, Burnley and Notts County boss to remain on the South Coast.
"I think what needs doing is to tie down the manager to a longer contract and keep him at the club," he told the Portsmouth News.
"I think he has done a magnificent job. Last year he was given peanuts and he delivered.
"We even had an outside chance of the play-offs at one point. I think the gaffer is as good as anyone I have worked with.
"I also don't think he has ever had the backing that other managers have had. Tony Pulis had a tremendous chairman behind him and great backing (at Stoke).
"He has ended up doing an unbelievable job. I am sure if the gaffer got the same backing off the owners he could be just as successful."