The Gunners broke the deadlock inside two minutes when Lacazette marked his league debut with a goal by heading home Mohamed Elneny's cross.
"Even if people will say, OK we conceded three goals".
Alexis Sanchez will miss at least the first two games of the Premier League season for Arsenal, with coach Arsene Wenger saying the absence is due to injury rather than doubts surrounding the forward's future at the club.
After so much talk of the 25th anniversary of the Premier League's breakaway and all of the core traits marketed as firing the competition, these two teams seemed determined to live up it, as they offered the most breathless and goal-laden start it has ever seen: two goals in four minutes, an bad lot of pace, and very little defending - especially in the air. Leicester then broke the tie in the 29th minute as top scorer from Leicester's Premier League winning season, Jamie Vardy opened his 2017-18 account with a stunning volley with his left foot.
While some fear the spending is unsustainable and will put clubs' long-term stability at risk, the 25th year of the Premier League era should deliver a title race more fiercely contested than ever.
It was an exciting game, the neutrals will have had a good time and both sides will take positives.
That goal should have been the one that woke Arsenal up and given them the need to take control and run away with the game, but, instead, it was Vardy who struck again to give Leicester the lead back in this back-and-forth game.
"Why hasn't he just said I'm staying for one more season?" To lose in the manner we did is very disappointing.
Mahrez saw an effort tipped over by Cech as Leicester looked to regain their advantage - something they did from the resulting corner as Vardy headed home the Algerian's set-piece.
The Serie A side have now said they will not return with an improvement on the offer that was rejected and, while he remains a Leicester player, Shakespeare is more than happy to utilise the 2016 PFA Player of the Year.
"They are not anxious about the money because they aren't the ones getting it".