The BBC pundit backs Newcastle to win 2-1 and take another step toward safety.
The already-relegated Villans have nothing but pride to play for, but even that does not appear to be much of an incentive as the West Midlands club bring an 11-match losing streak into their clash with Rafael Benitez's side.
Five of those defeats have come under caretaker boss Eric Black following Remi Garde's sacking in March, and Lawrenson finds it "very strange" that the club are yet to name a successor to the Frenchman.
In contrast, the Magpies boosted their survival hopes by beating Crystal Palace 1-0 last time out to move 17th in the table, one point clear of Sunderland and Norwich City who both have a game in hand over United.
Newcastle host Tottenham Hotspur on the final day in a fixture which Spurs will have nothing to play for if they beat Southampton on Sunday and secure a second-place finish ahead of Arsenal, and Lawrenson believes that could be key in the battle for survival.
"I find it very strange that Aston Villa have not appointed a new manager yet," he told BBC Sport.
"He could learn so much from the remaining games of this season - like last week, when they were 2-0 up against Watford and still lost - as well as from watching the players in training, talking to them and just being around them.
"I think their battle for survival will go right to the final day, and the fact Newcastle are playing Tottenham at home will definitely help them if Spurs have got second place sewn up by then. 1-2."