The Three Lions recently returned from a five-day warm-weather training camp in Portugal and play Peru in a friendly on Friday before jetting off to Miami.
Hodgson's side then play Ecuador on June 4 before facing Honduras three days later, both at the Sunlife Stadium, before they depart for their base at Rio de Janeiro's Royal Tulip Hotel.
Hodgson has picked a youthful-looking squad for his 23-man lineup, with the average age just 26, and the likes of Adam Lallana, Luke Shaw, Jordan Henderson, Raheem Sterling, Ross Barkley and Rickie Lambert all have less than 10 caps each.
However, speaking in his column in The Mirror, Lawrenson believes that their pre-tournament work has been exemplary so far.
He said: "Whisper it quietly but everything is falling into place 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."
Hodgson's side begin their World Cup campaign against Italy on June 14, before they play Uruguay and Costa Rica on June 19 and 24 respectively.