The France international, who joined from Lyon in a £46.5m deal last week, came on as a second-half sub and netted 15 minutes later to mark his first appearance with a goal.
Per Mertesacker had earlier found a way through against the reigning A-League champions, though it took until seven minutes from time to kill the game off thanks to Lacazette's poacher instincts.
The visitors opened their scoring account for the summer with less than five minutes on the clock, courtesy of a smart hooked finish from Mertesacker to help Mesut Ozil's uncleared corner past Andrew Redmayne.
Krystian Bielik climbed highest to nod a corner onto the roof of the net and Danny Welbeck was brilliantly denied by a Sebastian Ryall block in front of goal, as the Gunners cruised through the opening 45 minutes.
Despite all their dominance, the Premier League outfit could well have been pegged back 34 minutes in as, from their only serious attack of the half, Sydney hit the post through Matt Simon's sliding shot after Joshua Brillante's effort was parried into his path.
Arsenal, utilising a three-at-the-back system in this first pre-season outing, really should have been more than one goal to the good at the break, with Chris Willock - one of three senior debutants - waltzing his way through but failing to get the beating of Redmayne when one-on-one.
The second half proved to be slightly more evenly matched but it was still Arsenal who were creating the better openings, seeing chances come and go for Reiss Nelson and Cohen Bramall, both of whom impressed during their 70 minutes or so on the field.
Half-time replacement Emilliano Martinez instantly had more work to do than Petr Cech, keeping out Chris Zuvela's edge-of-the-box drive and also remaining alert to block Charles Lokolingoy's deflected effort.
There was a moment of controversy just short of the hour mark, with the referee wrongly pointing to the spot after Walcott's shot was blocked in front of goal by the back of Ryall - not the arm, as the official claimed.
Despite Sydney's protestations, not helped by a replay being shown on the big screen, the spot kick was still awarded, though Redmayne was again the hero to keep out Welbeck's attempt.
Walcott saw another opening come and go, this time shooting straight into the path of Redmayne, while substitute Alex Iwobi's shot was hit low and hard but did not find a way past the inspired stopper.
The Sky Blues, backed to match their feat of last season by winning the A-League crown in 2017-18, were giving a better account of themselves in the second half but desperately relying on their keeper to keep the scoreline down.
Iwobi pulled the ball back and Lacazette was waiting from seven yards out to divert the ball past Redmayne, ensuring that Arsenal are up and running with a convincing win.