Arsenal will take on United away from home at Old Trafford in the Premier League on Sunday afternoon.
Former Liverpool defender Lawrenson has backed the Gunners to register a 2-1 victory.
“The Gunners played well against Barcelona but lost out to a team with the best front three I have ever seen,” the former Republic of Ireland international told BBC Sport. “United's attack does not quite carry the same threat, does it?”
Arsenal will head into the game against United on the back of a 2-0 defeat to Barcelona at the Emirates Stadium in the first leg of the Champions League last-16 tie.
The Gunners will be determined to bounce back from that defeat and pick up all three points at Old Trafford.
The North London outfit are in better form than the Red Devils at the moment and also have a better team.
Arsenal are aiming to win the Premier League title this campaign, while United have top-four ambitions.
The first goal will be key. If Arsenal get it, then it is hard to see Arsene Wenger’s side dropping all three points.
Lawrenson has also told BBC Sport that he feels sorry for United manager Louis van Gaal.
The Dutchman has come under pressure due to his side’s disappointing performances and results this season.
“I am starting to feel a little bit sorry for him because he has been a great manager with a fabulous record, but that was yesterday and football has moved on so much,” said Lawrenson about Van Gaal.
“The days of being solid, staying in position and trying to pick the opposition off have gone. You need to have pace and the ability to tear through teams in the last third, and Van Gaal has not really grasped that. He was the right man for United, but his time was five or 10 years ago."