Lawrenson said that the time for him to leave was after Ireland's disappointing performance at last summer's European Championships.
"He should have left after Euro 2012 because Ireland were a disaster during the tournament," he told BBC Sport. "He got it completely wrong and it was time to rebuild last summer.
"It was always going to be a difficult [World Cup qualifying] group, the best you could realistically hope for was second behind Germany.
"If they had got somebody new last summer then they could have got new players in during this qualification period and if they came second and got in the playoffs it would have been a bonus."
The FAI have revealed that the nationality of the new manager does not matter to them.