Lacazette hammered into the top corner after a superb run to score the first goal of the tie in nearly 170 minutes of action and set up an encounter with Viktoria Plzen in the next round.
The French giants were given the upper hand when Chornomorets defender Evgeniy Zubeyko was dismissed four minutes before the goal, and the visitors can perhaps count themselves unlucky after playing their part in an intriguing encounter.
Lyon boss Remi Garde opted to restore a number of first-team players to the starting line-up, having largely selected a second string squad in the first leg.
However, much like the fringe players, Lyon's stars found their Ukrainian opponents a tough prospect in a first half of few clear-cut chances.
Oleksiy Antonov perhaps should have done better after heading over from close range, while at the other end Chornomorets goalkeeper Yevhen Past did well to tip Gueida Fofana's effort from just outside the area round the post.
Past's opposite number Anthony Lopes had to be on his guard to keep out Oleksiy Gai's effort while the visitors continued to attack after the interval, with Zubeyko pushing forward from full-back and firing over from distance.
The best chance of the match also fell to Chornomorets, for whom Markus Berger headed against the post from Ivan Bobko's corner.
Lyon came battling back and Steed Malbranque forced Past to tip his effort from more than 30 yards round the post.
Their hopes of victory were boosted when Zubeyko was given his marching orders after a cynical challenge on Fofana earned him his second booking, having received his first yellow card in the opening half.
Les Gones took full advantage by scoring four minutes later.
Clement Grenier fed fellow France international Lacazette, who cut inside from the left before expertly firing past a helpless Past.