France Under-21 striker Lacazette netted his maiden Champions League goal in the 58th minute as Lyon, who only made this stage for the ninth straight time after a 7-1 thrashing of Dinamo Zagreb, gained a victory they just about deserved.
APOEL, the first Cypriot team to reach the last 16 having topped a group featuring Zenit St Petersburg, Shakhtar Donetsk and Porto, had little to show for themselves offensively as they waited for the perfect counter-attack that never materialised.
"We expected this kind of game but I wish we had been more efficient. I now hope we will not regret it after the second leg," Lyon coach Remi Garde, whose side lost 2-1 at home to lowly Caen on Saturday, told France's Canal+ TV .
"They were supposed to have chances on counter-attacks and they did not get any, it's because we also defended well."
Lyon, who will travel to Cyprus for the second leg on March 7, could have gone ahead early on but were denied a possible penalty in the third minute after Ederson appeared to have been brought down by goalkeeper Dionisios Chiotis in the box.
The hosts piled on the pressure thereafter but APOEL held on thanks to their stout defence.
Lacazette dribbled past two defenders on the half-hour mark but fired wide with only Chiotis left to beat.
The forward had another chance five minutes before the break but his fierce shot was clawed away by Chiotis.
The second half started like the first one ended, with Lyon pushing hard for the opener.
Ederson dribbled past Chiotis, slotted the ball towards the empty net only for Paulo Jorge to clear off his line.
Lacazette finally broke the deadlock when his curled shot took a deflection off an APOEL defender into the far top corner.
"I was asked by the coach and my partners to take my responsibilities and to try a lot of things, that's what I did," said the goal-scorer, one of a bunch of youngsters being blooded this term by Garde.
Jimmy Briand, who replaced Lacazette right after his goal, sent over a perfect cross but Ederson's header went just wide as Lyon missed out a golden opportunity to double the tally.
APOEL had their only chance with two minutes left but France goalkeeper Hugo Lloris tipped an Esteban Solari attempt over the bar with his only actual save of the night.
The Cypriots have been the surprise packages of the competition this year having been rank outsiders but their strong defence will have to be combined with more of an attacking threat in Nicosia if their fairytale can continue.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.