One sign depicted a woman above the word "kitchen" and another showed a man alongside the word "stadium".
Lyon's president said on Twitter the club were investigating the incident.
Lille have since confirmed their home match against Lorient on Saturday will be free for all women, saying: "Ladies, you are welcome with us."
Lyon's women's team have won the French title 14 times and their captain Wendie Renard highlighted the banners saying: "Lyon supporters... can you give me an explanation for that banner? The men at the stadium, the women in the kitchen?"
Club president Jean Michel Aulas replied: "The club will get tough and will file a complaint against the creator of this banner."
Lyon, who are fourth in the league, lost the match 2-1 at Parc Olympique Lyonnais.
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