Lacazette score twice to help Arsenal win against West Brom at the Emirates on monday evening.
The Gunners now sit in seventh place in the Premier League table but have hit a purple patch since the away losses to Stoke and Liverpool in August.
Arsene Wenger's side are unbeaten in September and have kept clean sheets in all but one of this month's games.
"There was no feeling of panic in the team," said Lacazette. "We knew that working together would pay off. During the month of September we have reconstructed ourselves defensively. We won [against West Brom] and we won with a clean sheet."
With his brace, Lacazette became the first Arsenal player to score in his first three home games since Brian Marwood in 1988.
3 - A. Lacazette is the first Arsenal player to score in his first 3 home league apps for the club since Brian Marwood in Sept 1988. Gunner. pic.twitter.com/9Q8pwxwTEc
— OptaJoe (@OptaJoe) September 25, 2017
The France international added: "They said I [equalled Marwood], but I am not looking for this particular type of record but more stability with the team."
Lacazette, however, seemed less happy when he was selected for a random drugs test and took to social media to let his feelings known.
2 goals so.. doping control ?? well done guys #AFCWBA #Coyg #Arsenal pic.twitter.com/kO5dtHfyRX
— Alexandre Lacazette (@LacazetteAlex) September 25, 2017
He jokingly suggested that he was only tested because of his impressive performance on the night.