Solskjaer is on the verge of breaking his semi-final voodoo after Manchester United beat Roma 6-2 in the first leg of their Europa League last-four tie on Thursday.
They are sitting second in the league table with five games left in the season and are looking good to make sure that they finish runners-up to probable champions Manchester City.
The Red Devils will host Lawrenson’s former club Liverpool on Sunday as they look to deal a potentially fatal blow to their rivals’ top four hopes.
Lawrenson, looking ahead to the game, stressed that the only thing Solskjaer needs to do is to make sure Manchester United continue to win games in some sort of style and ignore the talk about the United Way.
The former Liverpool star believes his soft-spoken nature is often mistaken for being passive, but feels it is clear that Solskjaer is not afraid of taking the hard calls as a Manchester United manager.
He insisted that it would be a great season for the Red Devils if they win the Europa League and finish second in the Premier League.
Lawrenson said on LFC TV: “I think he has done a really good job.
“It’s difficult circumstances because every time they get a new manager he has to play the United Way but what on earth is that?
“The days of Best, Charlton and Law and all those guys are long gone. What he has to do is win games and try and win them in some kind of style.
“What did you say, one defeat in 27 in the Premier League? It is outstanding.
“Because he is soft-spoken and obviously he is a really nice fellow, people think maybe the players run all over him but they obviously don’t.
“He is not frightened to make decisions, look at the thing with the goalkeepers [David] de Gea and [Dean] Henderson.
“I think he has done a very good job and if they win the Europa League and finish second in the division, which I think they will, I think that goes down as eight out of 10.”
Manchester United will hope to beat Liverpool at Old Trafford on Sunday and further tighten their grip on second place in the league.