The disciplinary commission for the French League (LFP) have said Lyon must play their Ligue 1 games behind closed doors until a ruling is made on Sunday evening's abandoned match against Marseille.
Definitive sanctions are expected to be made by December 8 with Lyon's next home game against Reims on December 1. Dimitri Payet missed Marseille training on Monday. According to L’Equipe, four arrests were made following the match.
"The culprit was arrested. There was no risk that things could get aggressive again," Lyon president Jean-Michel Aulas said.
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"I think we are well organised here in terms of security. We think the game could have resumed without any problem."
Lyon said in a statement on Monday "they want the criminal and administrative sanctions to be exemplary".
"The institution intends to be able to strike off the individual for life if the league and the courts give the club the means to do so," read the statement on their website.
"Olympique Lyonnais and its president will participate in all analysis, work and proposal meetings so that this type of aggression never happens again and allows our football to take place in optimal security conditions."
Fan violence has been a recurring problem in French football this season.
Nice were docked two points after their players and fans clashed during their game against Marseille in August. Payet was struck by a projectile during the match with the former West Ham playmaker throwing the item back towards the crowd.
The northern derby between RC Lens and Lille in September also saw trouble. Rival fans threw objects at each other before people ran on to the pitch, prompting riot police and stewards to step in. Violent incidents have also taken place at Montpellier, Angers, Marseille and Saint-Etienne this season.
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French Sports Minister Roxana Maracineanu said such incidents are putting French football in danger.
"Everyone must understand that it's the survival of French football that's at stake," she said.
We can't allow that a broadcaster, who has bought rights, must keep the conversation moving for more than an hour like they did last night, when we don't know if the match is going to continue, it's a world where millions of euros are at stake.
"We've helped the football world during the health crisis to allow the return of fans in the stadiums, we can't allow things like that to happen."
Lyon-Marseille fixture abandoned after 'cowardly assault' on Payet
Lyon-Marseille halted after Payet struck by water bottle thrown from crowd