Although their title challenge has faltered in recent weeks, Arsenal will face Wigan Athletic for a place in the FA Cup final next weekend and Lawrenson says that if they go on and lift the trophy, it would be the perfect time for Wenger to exit.
"I'm a huge admirer of Arsene Wenger. He has done a wonderful job for many years at Highbury and the Emirates," he wrote in The Mirror.
"But it is looking as if the magic is gone. He is no longer working the miracles that he used to and Arsenal's fans are becoming increasingly frustrated by that.
"Delivering the FA Cup might just be the best way to bring the curtain down on what used to be the best show in town."
Arsenal have won three Premier League titles and four FA Cups under Wenger, but have not won a trophy since 2005.