The French side claimed a shock 2-1 away victory in their Champions League opener against the Premier League champions, seen as one of the favourites, with goals from Maxwel Cornet and Nabil Fekir at the Etihad Stadium.
Lyon have issued a statement saying they condemn the incident and will deal with the individual sternly.
The club said: “Olympique Lyonnais has seen a video that has circulated on social networks.
“The supporter in question is being identified by the services of Olympique Lyonnais.
“As soon as he is identified, he will be excluded for life at Groupama Stadium (Lyon’s home ground) and travel for club matches.”