The Merseyside outfit will start the new Premier League season with a clash against the Championship winners.
Liverpool FC finished in second place and a point adrift of champions Manchester City last term.
Jurgen Klopp’s side will be looking to go one step better in the current campaign.
Liverpool FC won 17 of their 19 home games in the Premier League last term, only dropping points in stalemates with Manchester City and Leicester City.
Norwich, on the other hand, won the Championship with a five-point advantage over their closest rivals Sheffield United.
Former Liverpool FC defender Lawrenson is backing the Merseyside outfit to ease to a comfortable 2-0 victory over Norwich at Anfield on Friday night.
“I will be at Anfield for this one, and I am expecting Liverpool to win,” Lawrenson told BBC Sport.
“They have got the Super Cup on Wednesday but I am expecting Jurgen Klopp to pick a strong side, and start with his regular front three even though Sadio Mane only came back to training this week.
“Like any promoted team, Norwich’s problem is not so much whether they will concede goals – which I think they will – it is whether they will get enough goals to be competitive.
“We know how well Teemu Pukki did in the Championship, but will he score enough in the Premier League? I don’t think so – I don’t think he will get 10 league goals this season.
“The Canaries will be full of running in this game, but I just don’t see them causing Liverpool many problems. Of the three promoted teams, I think they are going to have the toughest time of it over the next few months.”
Liverpool FC didn’t make any notable signings in the summer transfer window despite winning the Champions League last season.
The Reds signed 17-year-old Dutch defender Sepp van den Berg, Fulham teenager Harvey Elliott and West Ham goalkeeper Adrian.
The Merseyside outfit allowed English striker Daniel Sturridge and Spanish defender Alberto Moreno to leave the club on free transfers.
Liverpool FC haven’t won the Premier League title but have finished in second place on four different occasions.
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