Lacazette's stunning 36th-minute free-kick put the English club through to a final four meeting with Spanish side Valencia.
However, coach Unai Emery warned the Gunners to expect a strong response in the second leg in Naples on April 18.
The Gunners have won just five Premier League games on their travels all season, losing 1-0 at Everton last weekend to damage their chances of securing a top-four finish.
Napoli have strengthened their grip on second spot, 15 points behind runaway leaders Juventus in Serie A.
Juventus still 15 points clear despite their 2-0 defeat to Genoa, which was their first of the season.
Unai Emery's team will host Napoli, who are currently second in Serie A, at the Emirates Stadium in the first leg on April 11.
Juventus are on course to claim their eighth straight Serie A title after stretching their lead to 16 points.
The Polish forward was given his first Milan start at San Siro and it took him less than 11 minutes to open his Rossoneri account.
Izzo headed in the only goal to get Torino back winning after their defeat last weekend to Roma.
Napoli have 47 points from 20 games and are now seven ahead of third-placed Inter Milan who were held to a goalless draw at home by Sassuolo on Saturday.
Napoli's French-born Koulibaly was targeted by monkey noises and racist chants at the San Siro, before being sent off for sarcastically applauding referee Paolo Mazzoleni.
Four Napoli fans were injured and at least three people arrested.
Liverpool vs Napoli: Carlo Ancelotti frustrated as team denied Champions League "cherry on the cake"
In the end, Napoli finished level on points with Liverpool but were edged out on the third tie breaker, goals scored. That meant every point and goal in the group proved to be decisive.
Mohamed Salah's stunning solo effort put the hosts in front 11 minutes before half-time, but Liverpool were nearly made to pay for their profligacy in missing a series of second-half chances.
Ancelotti's team closed the gap on Juventus to eight points after the seven-time reigning champions continued their unbeaten run with a 1-0 win over Inter Milan on Friday.