In a highly-charged statement, Lyon warned of French clubs facing cumulative losses of €900million, highlighted bankruptcy fears, and expressed concern over "football lovers who are deprived of their passion".
"There remains time, until May 25, to walk back and avoid an immense rout of the French championship," the statement said.
The Ligue 1 season was abandoned in late April after French authorities decreed there would be no live sport in the country until at least September.
Lyon missed out on qualifying for Europe through Ligue 1, finishing seventh in the curtailed campaign, and must win the delayed Champions League to earn a return to the competition next season.
The club said they had "made several credible proposals" on how to complete the 2019-20 French season, including giving over the months from September to December to ensure all fixtures are played and insisted they were not acting purely out of self-interest.
"But, on April 30, the LFP [Ligue de Football Professionnel] suddenly decided to definitively stop the French professional championship," Lyon's statement added, "without taking into account all of UEFA's recommendations, or giving itself time to observe what our dozens of neighbors were planning: relaunching the championship while working on an entirely exceptional health protocol to protect the various players in football."
Lyon warned the gap between French football and neighboring countries could grow because of the abandoned season, with the statement ending in a desperate plea.
It read: "We all love football, we all love this game. We love the values it conveys, the passion it exudes. Football is part of our life and our cultural heritage. The championship is our ritual.
"We absolutely must take care of it as all those did who came before us. We are their heirs."
The statement was not signed but was firmly in keeping with recent messages from club president Jean-Michel Aulas.
Aulas, meanwhile, told French broadcaster RTL on Saturday that Lyon's European away clash with Juventus had been rescheduled for August 7.
It now appears the trip to Turin may not be as inked in as Aulas indicated, with Lyon rowing back on the president's comments.
Lyon said on their official website on Sunday that a date for the last-16 second leg "has not yet been confirmed, contrary to what has previously been stated", saying such an announcement would come from competition organizers UEFA.
Lyon claimed a 1-0 win in the first leg in France in February thanks to a goal from Lucas Tousart. The competition was suspended in March due to the coronavirus crisis.
Aulas on Saturday predicted Lyon and PSG would "be massacred" by their European rivals if the competition resumes in August, given they will be out of match practice.
Leagues in England, Italy and Spain are pushing to resume within weeks in an effort to complete the domestic 2019-20 season, while Germany's Bundesliga will restart this month.