The former Liverpool defender claimed that the "magic is gone" from Wenger, and he stated that this campaign could be the Frenchman's last at the club that he has managed for 18 years.
Lawrenson told The Mirror: "I'm a huge admirer of Arsene Wenger. He has done a wonderful job for many years at Highbury and the Emirates.
"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. Maybe Arsene himself could turn around and say: 'Thanks for everything, I'm going to move on'."
The Gunners are currently fourth in the Premier League.