The Gunners, already leading 2-0 from last week's opening 90 minutes in North London, extended their advantage through Lacazette's 36th-minute free kick.
Both teams wasted chances in the remainder of the match and in the end it was a safe passage through for the visitors, who will face Valencia in the last four.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
That two-goal margin of victory could come in handy as the visitors have lost both away knockout-round ties in this season's competition, while their Italian opponents are unbeaten in five home European fixtures this term, scoring 10 goals and conceding just two.
STARTING XI: Meret; Maksimovic, Chiriches, Koulibaly, Ghoulam; Callejon, Allan, Ruiz, Zielinski; Milik, Insigne
SUBS: Ospina, Malcuit, Rui, Mertens, Verdi, Hysaj, Younes
STARTING XI: Cech; Sokratis, Koscielny, Monreal; Maitland-Niles, Torreira, Xhaka, Kolasinac; Ramsey; Lacazette, Aubameyang
SUBS: Ozil, Iwobi, Elneny, Guendouzi, Leno, Mustafi, Mkhitaryan
NAPOLI SUBS: Ospina, Malcuit, Rui, Mertens, Verdi, Hysaj, Younes
ARSENAL SUBS: Ozil, Iwobi, Elneny, Guendouzi, Leno, Mustafi