The Gunners suffered a significant blow to their hopes of winning the title this season when they were beaten 3-2 by Manchester United at Old Trafford on Sunday afternoon.
The result was compounded by the fact that both Tottenham and Leicester City won their games to move clear of the north London side in the table.
Arsenal are now five points behind leaders Leicester and three behind local rivals Tottenham heading into the final 11 games of the season.
Much has been made of Arsenal’s disappointing performance at Old Trafford on Sunday, but former Liverpool man Lawrenson is tipping the Gunners to rediscover their winning form against the Swans on Wednesday at The Emirates.
Writing in his column for BBC Sport, Lawrenson said: “Swansea put up a good fight against Tottenham and Lukasz Fabianski made some great saves to keep them in it, but they still lost and it is hard to see them getting anything at Emirates Stadium.
“To have any hope of winning the title, Arsenal quite simply have to win.
“If they don’t, for whatever reason, their fans are going to have a real moan. Even if they do, there are going to be a lot of people doubting the Gunners ahead of Saturday’s north London derby.”
Arsenal have not won the title since the 2003-04 season.
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