The Gunners head into the game looking to get their Premier League bid back on track after having lost three of their last four games in the top flight.
Arsenal are currently fifth in the table but would move above Liverpool into fourth place if they can win their two games in hand over the Reds.
However, former Liverpool star Lawrenson is backing Arsenal to drop two points against Tony Pulis’ men at The Hawthorns this weekend.
Writing in his column for BBC Sport, Lawrenson said: “West Brom have lost two on the trot, and their performances in those defeats were disappointing as well.
“The Baggies are yet to beat a top-seven team this season but I am expecting a response from them on Saturday after their recent displays.
“They don’t have the attacking players to really unhinge the top sides but you can see why they do so well against everyone else because they are strong, well organised and committed.
“I think Tony Pulis’ side have probably reached their ceiling, if you like, in eighth place – but that is still a big achievement. They know what they are good at, and it works.
“I am still not quite sure what to expect from Arsenal, especially on the road, but on the upside for the Gunners it has been a quiet week for Arsene Wenger after they reached the FA Cup semi-finals.
“It still feels like Arsenal are in limbo, though, because there is so much to be decided about Wenger’s future, and Mezut Ozil and Alexis Sanchez’s contracts too.
“They have a mixed record at The Hawthorns with only one win in their past three league visits, and I don’t see them leaving with three points this time either.”
Arsenal are through to the FA Cup semi-finals after a 5-0 win over Lincoln last weekend. The Gunners will take on Pep Guardiola’s Manchester City side at Wembley next month for a place in the FA Cup final.
The Gunners finished second and without a trophy in the top flight last season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news