The France striker, who has had a difficult start to the season, netted his second league goal on the stroke of halftime to send OL fourth in the standings with 15 points from nine games.
They trail leaders Paris St Germain, who host bitter rivals Olympique de Marseille on Sunday, by five points, while Reims slipped to fifth, also on 15 points.
Lacazette, who earlier this week criticised club president Jean-Michel Aulas for disclosing details of their contract extension, had scored his first goal of the season two weeks ago in a 1-1 draw at Marseille.
That was a penalty and he had another spot kick on Saturday after being brought down by Jaba Kankava in the 41st minute, but his attempt crashed onto Johny Placide's bar.
Lacazette, last season's top scorer with 27 goals, made up for his mistake three minutes later.
After a one-two with Claudio Beauvue, he opened the scoring with a low shot that took a slight deflection off Franck Signorino.
Beauvue came close to doubling the lead but his header smashed against the crossbar.
Lyon, who lost defender Milan Bisevac to injury after six minutes, controlled the rest of the match and put a bad week behind them after they lost 1-0 at home to Valencia in the Champions League on Tuesday.
In-form Nice could move up to second if they beat Nantes at home later on Saturday.
(Reporting by Julien Pretot; Editing by Alan Baldwin)
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