The Seagulls are currently sixth in the table after making an impressive start to their Premier League campaign, and would have gone top had they managed to secure all three points against rivals Crystal Palace on Monday evening.
For their part, the Gunners endured a dreadful start to the season, but have since registered three straight victories to elevate themselves up to 10th.
And Lawrenson believes that they will move level on points with Albion by winning Saturday’s meeting between the two clubs.
Speaking on BBC Sport, he said: “Brighton missed the chance to go top of the table on Monday but the way they snatched a point right at the end of their game against Crystal Palace will still give them a big lift.
“The Seagulls have made a really impressive start to the season, but Arsenal are on a bit of a roll at the moment.
“That run won't last for too long - not a lot has changed about the Gunners, really, because I still think they will go on streaks of good or bad results just like last season - but they will be smiling on Saturday evening anyway.”Lawrenson has opted for a 2-0 Brighton loss.
Albion have endured mixed fortunes against the Gunners in recent times.
Last term, Graham Potter’s men lost both of their encounters with the north London side, but the season before that, the Seagulls took six points from a possible six against Saturday’s opponents.
We’ve gathered the best of today’s Premier League chatter below…

1. Man United urged to Rice and Soucek
West Ham United's Declan Rice and Tomas Soucek are both better than Manchester United's other midfield options, according to former Manchester City star Trevor Sinclair. (TalkSPORT) (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield

2. Traore close to new deal
Adama Traore is reportedly close to signing a new contract with Wolves amid interest from Liverpool and Tottenham. (Daily Mail) (Photo by Alex Davidson/Getty Images) Photo: Alex Davidson

3. Hammers keen on Lewis-Potter
West Ham have kept tabs on Hull City’s talent after signing Jarrod Bowen and now want to sign youngster Keane Lewis-Potter. (TEAMtalk) (Photo by George Wood/Getty Images) Photo: George Wood

4. Reds want Diaby
Liverpool are looking to rejuvenate their forward line and have identified Bayer Leverkusen’s Moussa Diaby as a leading target. (Calciomercato) (Photo by Ian MacNicol/Getty Images) Photo: Ian MacNicol