The Gunners head into the game looking to get back to winning ways in the top flight after their goalless draw with Chelsea in the first leg of their League Cup semi-final clash on Wednesday night.
Arsenal were dumped out of the FA Cup at the hands of Nottingham Forest last weekend and were held to a 2-2 draw by Chelsea in the top flight before that.
And former Liverpool FC star Lawrenson is tipping the Cherries to further frustrate the Gunners and dampen their hopes of a top-four finish by claiming a point against them this weekend.
Speaking to BBC Sport, Lawrenson said: “Arsenal’s defence of the FA Cup ended in style, if you can call it that, at the hands of Championship side Nottingham Forest on Sunday.
“Bournemouth are still in it, but only just after battling back to draw 2-2 with League One leaders Wigan
“I’m going to go with another draw in this game too, because Arsenal are pretty inconsistent away from home – which is a worry.
“It should be quite an open game, but I can see the Gunners dropping more points.
“I don’t see manager Arsene Wenger’s touchline ban having anything to do with it, though, especially at Bournemouth where the stands are so close to the pitch. He can still communicate with his players during the match and speak to them at half-time as well.”
Arsenal are aiming to try and break back into the top four this season after the disappointment of their fifth-placed finish last term left them playing Europa League football.
The north London side are currently in sixth place as they try to get back into the top four this season under Arsene Wenger and bring Champions League football back to The Emirates.
The Gunners have not won the Premier League since their famous unbeaten triumph in the 2003-04 campaign.
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