The Foxes are currently five points clear of nearest rivals Tottenham at the top of the Premier League, ahead of the visit of Southampton to the King Power Stadium on Sunday.
And although Claudio Ranieri's men face trips to Old Trafford and Stamford Bridge before the end of the season, Lawrenson is convinced they will still be at the league's summit at the end of it all.
Speaking to BBC Sport, he said: "I said before the international break that Leicester are on course to win the title and I don't see anything in their remaining games to change that.
"Yes they have to go to Old Trafford and Stamford Bridge in May, but forget the clubs they will play and look at their teams and their league position.
"Manchester United are ordinary and Chelsea are poor, while Leicester are the best team in the league and have been all season."
City have won just one of their last six Premier League games ahead of Manuel Pellegrini's departure at the end of the season, with Lawrenson adding that the Chilean's replacement - Pep Guardiola - may well be about to take over a club competing in the Europa League next season.
"As far as the top four goes, I just don't think Manchester City are going to get in the Champions League places - the whole club looks as flat as a pancake," he added.
"I think City should just say to Manuel Pellegrini now, in the nicest way, 'thank-you very much and goodbye', and put someone else in charge until the end of the season.
"It is a bit like 'Waiting for Godot' now. We are all just waiting for Pep Guardiola's arrival in the summer and I would just say to Pellegrini 'don't waste any more time here with these players, because some of them have given up on you'.
"It has turned into a horrible situation and by keeping him hanging on it is just prolonging the agony for everyone. I know they are still in the Champions League, but the whole thing has just become a bit embarrassing."
Despite currently enjoying a five-match unbeaten run in the Premier League, Lawrenson also predicts that West Ham United will just miss out on Europe this season and finish in sixth.