The two clubs currently occupy the bottom two spots in the table, with Daniel Farke’s Canaries still awaiting their first point of the campaign.
For their part, Sean Dyche’s men have drawn two of their opening six matches, and came agonisingly close to breaking their winless streak in last weekend’s 2-2 draw against Leicester City.
But Lawrenson is of the opinion that they can finally get themselves on the board at Turf Moor on Saturday.
Speaking to BBC Sport, he said: “This is 19th versus 20th and neither side have managed a win yet, but Burnley have looked far more like getting one than Norwich have so far.
“Too often, the Canaries have been out-thought and out-gunned. They haven't even got a point on the board after six games and there haven't been too many moments when they have looked like getting one either.
“Burnley, in contrast, have been much more competitive, even when they have lost.
“Sean Dyche is going to have work cut out to keep the Clarets out of trouble but, from what I've seen of both teams, they should take the points here.”
Lawrenson has opted for a 2-1 Burnley win.
Burnley enjoyed a good record against Norwich when the Canaries were last in the top flight, beating them 2-0 both home and away in 2019/20. In between those two matches, however, they did lose an FA Cup tie against Farke’s side, slumping to a 2-1 defeat.