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Lille's defeat to Nice is their worst home league loss since 2017.
Lille were swept aside last season by their manager Christophe Galtier, who saw Nice win big at Stade Pierre Mauroy.
After just 55 seconds, the defending champions were behind when Kasper Dolberg from Denmark turned in from close range.
Nice doubled their lead in five minutes with a long-range Hichamboudaoui effort.
Amine Gouiri scored a third goal from the penalty spot before Dolberg scored his second to secure the win and end Lille's worst home league loss since 2017.
Galtier, 54 years old, was appointed Lille's head coach just two days after winning their first French league title for a decade. They finished one point ahead Paris St-Germain.
He ended his three-and-a-half-year spell to take charge of Nice, who are owned by Ineos, the group chaired by British billionaire Sir Jim Ratcliffe.
Lille is 16th in Ligue 1 after drawing 3-3 against Metz in the season opener.
