The north London side have made a strong start to the new campaign under new manager Unai Emery after initially struggling in their opening Premier League fixtures.
Arsenal lost back to back games to Manchester City and Chelsea FC, before stringing together a run of six successive wins in all competitions under their new boss.
The Gunners will be aiming to make it five wins in a row in the Premier League on Saturday lunchtime when they host Watford at The Emirates in the top flight.
Meanwhile, Liverpool FC have been flying high at the top of the Premier League table under Jurgen Klopp and they have won all six of their opening top flight games under the German manager ahead of their trip to Chelsea FC on Saturday evening.
And Lawrenson has warned Arsenal that they will face a stern test against Liverpool FC when they host the Reds at The Emirates on Saturday 3 November.
Speaking to BBC Sport, Lawrenson said: “I don’t actually think much has changed about Arsenal under Emery – they are a good side, but they were a good side under Arsene Wenger, just not one of the best three teams in the country.
“It will be interesting when they come up against the big teams – like Liverpool on 3 November for example.”
Arsenal are aiming to try and break back into the top four this season after they finished sixth and without a trophy last term under Arsene Wenger.
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