However, he has been left out of the first XI in two of Arsenal's biggest games of the season so far - also starting on the bench against Liverpool at Anfield as Wenger's men lost 4-0.
Lacazette came on in the second half and scored his side's only goal of the game, and Shearer, the former Newcastle United striker, believes he should speak with Wenger to discover why he is not playing.
"He left him out at Anfield and again today, against your rivals," Shearer said on Match of the Day 2.
"You spend £50m on a striker and think he will make the difference in the big games.
"He has scored six league goals, more than double anyone else in that Arsenal team.
"He played Alexis Sanchez today, who doesn't want to commit himself to the football club, what does that say to Lacazette and his teammates?
"He has got every right to go and knock on Wenger's door tomorrow and say: 'Do you not fancy me or something?'"
The Gunners are currently sixth in the Premier League, 12 points behind leaders City.