Danish former Leicester City star Schmeichel made a series of key saves, including turning a Timothy Weah attempt onto a post, and Gaetan Laborde scored the only goal of the game at the other end for Nice.
It was a third match without defeat for interim Nice coach Didier Digard since he took over from the sacked Lucien Favre at the club owned by Ineos, current suitors of Manchester United.
The result ended an eight-game unbeaten run for Lille and dents their prospects of qualifying for Europe. Nice remain in mid-table but are now just six points behind them.
Lyon, another ambitious club enduring a difficult season, are above Nice on goal difference after claiming a 2-0 victory in Corsica.
Johann Lepenant put them ahead before ex-Arsenal striker Lacazette notched his 12th league goal of the season.
There were also wins on Sunday for Montpellier and Toulouse, while bottom side Angers lost 4-0 at Brest to suffer a Ligue 1 record-equalling 12th consecutive defeat.
Clermont and Nantes drew 0-0 in a game that did not feature a single shot on target.
Leaders Paris Saint-Germain host Reims later and can go five points clear at the top from Lens, who needed a late equaliser from substitute Adrien Thomasson to draw 1-1 at Troyes on Saturday.
Marseille could have moved above Lens on goal difference when they played Monaco in Saturday's late game but they also dropped points in a 1-1 stalemate.
PSG's opponents Reims are led by 30-year-old Belgian-born English coach Will Still and are on a 13-game unbeaten run.
