The Three Lions recently returned from a five-day warm-weather training camp, and they meet Peru this Friday before flying out to Miami for friendlies with Ecuador and Honduras on June 7 and 10 respectively.
Writing in his column for The Mirror, Lawrenson claimed that the squad's work so far has been exemplary.
He said: "Whisper it quietly, but everything is falling into place nicely for England ahead of the World Cup.
"And I was pleased to see Steven Gerrard joining the pundits' union at the Champions League final – a positive sign that England psychiatrist Steve Peters is making his presence felt in a positive way. Why should the England captain hide himself away for a month before the World Cup?
"It's a sign that Roy Hodgson has cultivated a sensible, relaxed atmosphere within the camp where Fabio Capello managed to run a five-star boot camp in 2010. There is no hint of any cliques, no battle for supremacy between players who believe one is more deserving of the captaincy than the other, no sniping about the manager's tactics."