The Gunners head into the game on the back of their 3-1 win over Valencia in the first leg of their Europa League semi-final clash at The Emirates.
Arsenal are currently in fifth place in the Premier League table as they chase a top-four finish, but they will need either Tottenham and Chelsea FC to drop points in their remaining two games to have any hope of overtaking them.
The north London side will have one eye on the Europa League as a potential route into next season’s Champions League.
And former Liverpool FC star Lawrenson is tipping the Gunners to claim a comfortable victory in front of their home fans in the Premier League at The Emirates on Sunday afternoon.
Writing in his column for BBC Sport, Lawrenson said: “Arsenal’s recent performances in the league have been very poor, as bad as anything we have seen from them in the past five years.
“Defensively they are probably the worst they have been for a while, no matter who Unai Emery brings into the team.
“Away from home they remind me of the latter seasons when Arsene Wenger was there and they would go to places such as Stoke and get turned over, and you never fancied them.
“The problem now is that you don’t fancy them anywhere on the road – every fixture looks difficult for them.
“At Emirates Stadium, things are usually much better. I know they lost to Crystal Palace in their previous home league game, but I would still fancy them to beat Brighton.
“The Seagulls couldn’t put two passes together in the first half against Newcastle but they were much better in the second half and could have ended up going on to win the game.
“I was at the Amex Stadium and I was impressed by Brighton midfielder Solly March when he came on for the second half. He really lifted the crowd and the whole atmosphere too.
“It is going to be very hard for them at Arsenal but I think the Seagulls will be safe anyway, because I do not see Cardiff getting six points from their final two games.
“If the Bluebirds get four points, which I don’t see happening either, then the Seagulls’ goal difference will still keep them up.”
Arsenal have endured an inconsistent first season under Unai Emery, but finishing in the top four or winning the Europa League would represent progress for the Gunners, who finished sixth and without a trophy in Arsene Wenger’s final campaign in charge last term.
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