The club has been deprived of a spot in a European competition for the first time in a quarter of a century.
It follows the decision of the French League to end the League 1 season, after the French government ruled all sport was banned until September.
As a result Lyon are judged to have finished 7th in the table with no chance of a European spot for next season.
The club claims the season could have been finished in the form of playoffs behind closed doors in August.
Club president Jean-Michel Aulas said they would seek "dozens of million" euros in damages.
"It's a big loss of opportunity that has a financial value that amounts to dozens of million euros, which will be claimed in damages," said Aulas.
"We see that these standings are illogical. I don't want to single out a club more than another but Nice played at home more than us and faced Paris St Germain (PSG) only once while we played them twice," he explained.
