The Red Devils decided to part company with Jose Mourinho last week after Manchester United suffered a humiliating 3-1 loss to bitter rivals Liverpool FC at Anfield.
Manchester United have turned to their former Red Devils striker Solskjaer to take over the reins from Mourinho for the remainder of the Premier League season.
The Champions League winner had an unhappy stint in charge of Cardiff City, but Solskjaer has established a promising reputation during his time at Norwegian club Molde.
Manchester United are in sixth place in the Premier League table and 11 points adrift of fourth-placed Chelsea FC in the race to secure a Champions League spot.
Former Liverpool FC defender Lawrenson is confident Solskjaer will make a winning start to his Manchester United reign against Cardiff in Wales on Saturday.
“Cardiff have won four of their past five home games but this is going to be a very tough game for them,” Lawrenson told BBC Sport.
“Whenever a new manager comes into any club, all the players are instantly far more focused.”
Lawrenson added: “I can guarantee you that in United’s training sessions this week, everything will have been really sharp and I would expect them to translate that into a convincing performance.
“Ole Gunnar Solskjaer was not a success when he was Cardiff manager in 2014, but this is a completely different situation for him.
“I think he will get results, but what happens next at United is going to be very interesting.”
Manchester United have already lost five times in the Premier League this season to raise questions about their ability to secure a top-four finish this term.
Liverpool FC, Manchester City, Brighton, West Ham and Spurs have all beaten Manchester United in the current Premier League campaign.
The Red Devils haven’t won the Premier League title since Solskjaer’s former manager Sir Alex Ferguson was still in charge.
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