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…
5. Hutton tips Leeds to cash in on Phillips
Alan Hutton has suggested Leeds United could cash in on Kalvin Phillips next summer to reinvest in new signings. (Football Insider) (Photo by George Wood/Getty Images) Photo: George Wood
6. Lacazette headed for Arsenal exit?
Arsenal will consider using Alexandre Lacazette as a makeweight in a deal for Sevilla's Youssef En-Nesyri in January. (La Razon) (Photo by Julian Finney/Getty Images) Photo: Julian Finney
7. Phillips expected to stay put
However, contrasting reports suggest that Kalvin Phillips is likely to sign a new long-term contract with Leeds United in the near future, with his agent supposedly suggesting that all parties are keen on striking a deal. (Telegraph) (Photo by Laurence Griffiths/Getty Images) Photo: Laurence Griffiths
8. McAvennie optimistic about Toon takeover
The Saudi-led takeover of Newcastle United will go through when arbitration starts up in January, according to former West Ham hitman Frank McAvennie. (Football Insider) (Photo by Catherine Ivill/Getty Images) Photo: Catherine Ivill