The Red Devils have taken 11 points from eight league matches, their latest match ending in a 1-1 draw against Southampton at Old Trafford on Saturday.
"With Moyes having failed to bring in a star name, it will be interesting to see whether Sir Alex reveals the players he would have signed had he not retired at the end of last season," Lawrenson wrote in The Mirror.
"It will be interesting, too, to see what he says about Wayne Rooney, who has been United's best player by a mile this season, because, having won just three of their last eight home games and with 13 points dropped from their eight matches so far this season, United are in real trouble. I'm starting to feel sorry for David as the job is beginning to look like a poisoned chalice."
United will turn their attention to the Champions League this week when they take on Real Sociedad on Wednesday.