The Gunners struggled to engineer clear-cut chances in a cagey first half at the Emirates but Lacazette broke the deadlock in style in the 56th minute.
Arsenal doubled their lead just three minutes later as Pierre-Emerick Aubameyang finished off a rapid counter-attack to seal the sides fifth victory on the bounce in all competitions.
Lacazette remained on the pitch for the remainder of the match while Aubameyang was substituted in the 69th minute, but Emery revealed that he considered bringing the Frenchman off before his wonder strike as Everton threatened.
Its not important, but yes, Emery replied when asked if he planned on replacing Lacazette.
At that point we needed a change to stop their attacking moments but then we scored and I decided to think again.
Emery praised summer signing Lucas Torreira for keeping his discipline after an early booking in what was his first Premier League start.
Torreira was on a yellow card and I was thinking how can he control the game in the last few minutes with this card against him? the Spaniard said.
But I think he did very well without the risk of losing another.