Lacazette had gone eight matches without a goal before he put the Gunners ahead in the 10th minute on Thursday with a stunning long-range strike.
Pablo Mari headed in the second from a corner before Eddie Nketiah finished off a stylish team goal a minute before half-time.
Arsenal, who had already qualified for the competition's last 32, conceded when Koya Kitagawa fired home early in the second half but Emile Smith Rowe added a fourth to stifle any hopes of a comeback.
Mikel Arteta made 11 changes from the side that lost 2-1 at home to Wolves in the Premier League last weekend and those involved made a high-tempo start.