Sunday's 4-0 rout over Tottenham Hotspur at Anfield put the Reds four points above City, who have two games in hand.
"I'd it to happen but I still don't think it will," Lawrenson wrote in The Mirror. "For some time now I've been saying that although Liverpool can win the Premier League they ultimately won't, and I still believe that.
"Don't get me wrong, their 4-0 destruction of Spurs to go top of the Premier League was another fantastic performance. The Reds have been magnificent all season, shooting their way out of trouble and that sends confidence right the way through the team.
"But for Liverpool to win the league they will have to turn eight wins in a row into 14. That is a massive ask. And I think Manchester City's deeper squad will just give them the edge."
City will travel to Anfield on April 13.