The Gunners have been in good form in recent weeks and have won their last six games in all competition under new boss Unai Emery after a difficult start to the new campaign.
Arsenal claimed a 3-1 win over Brentford at The Emirates on Wednesday night as they claimed their spot in the fourth round of the competition.
The north London side have also won their last four games in the Premier League after having lost their opening top flight games against Manchester City and Chelsea FC.
And former Liverpool FC star Lawrenson is backing Arsenal to continue their good form this time around.
Writing in his column for BBC Sport, Lawrenson said: “Arsenal have now won six games in a row in all competitions – OK, they have not beaten any big-hitters but you can only beat what is put in front of you, and they are doing that which is the most important thing.
“I am sure new Arsenal boss Unai Emery will be asked about the comments by Hornets’ striker Troy Deeney last season that the Gunners’ lacked the “cojones” for a fight after his side had beaten them.
“I think they will beat Watford and make it seven in a row.”
Arsenal are aiming to at least break back into the top four this season after they finished in sixth place and without a trophy under Arsene Wenger last term.
They have not won the Premier League title since their famous unbeaten triumph under Wenger back in the 2003-04 campaign.
Arsenal brought in Emery as their new manager after Wenger opted to stand down at the end of last season.
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