Lawrenson, who made 83 appearances in the Third Division for hometown team Preston North End in the '70s, gave his thoughts on the battle for Premier League survival, and he expressed his concerns on what relegation could mean for the bottom-of-the-table Clarets.
Speaking to FreeSuperTips, the former Republic of Ireland international defender also gave his thoughts on which other teams are at risk of returning to the Championship.
“I think Norwich will go down because I don't think they have enough to stay up," said Lawrenson, who helped the Reds become champions of England five times.
“Also, part of their planning is relegation and promotion because they're a small club who can't pay these fees other clubs can.
“They can live with that, the fans accept it, so I think they'll go.”
Burnley host relegation rivals Watford in a highly-publicised 'six-pointer' at Turf Moor on Saturday evening, with just a couple of points separating the two sides at the foot of the table.
Victory would see Sean Dyche's side climb above the Hornets and Newcastle United while moving to within a point of the Canaries, who will have played three games more.
Lawrenson continued: “I look at Watford and I think about Roy Hodgson because one thing players will tell you about when working with Roy is his coaching is all about closing down the space for the opposition.
“If they start to do that and make it more difficult, then they may get better results, but I don't think they'll do it."
He added: “Burnley do worry me, they never have in the past, but they worry me this time around.
“The finance with this American company that's bought them looks a bit flimsy, I'm told if they get relegated, they owe £60 million and I'm not sure where you're going to find that from.
“They've drawn a lot of games, they have an outstanding manager, but the problem is they keep drawing and they can't seem to win.
“I think this might be the year that Burnley go down.”
The Clarets have won just once this season and have drawn half of their 18 games this season in the top flight.
Should they get anything from the Premier League's only scheduled fixture this weekend they'll have bettered the start they had in 2018-19, but Lawrenson is still pessimistic about the club's chances of beating the drop.
He concluded: “The last time Burnley got relegated from the Premier League, they went into the Championship and spent more money than they did in the Premier League the previously season.
“They did all their training ground up and came back strong, but there's something about that club at the moment that doesn't seem right.
“It's not the manager because he's done an outstanding job, but they do worry me because I think they'll go through the trap door this time.”