Nineteen women sued Lyft this week, joining a growing list of people who say the popular ride-hailing service failed to prevent drivers from sexually assaulting them, then ignored the complaints.

The lawsuit is the latest to accuse Lyft of failing to enact basic safety measures that would have prevented the alleged assaults. After the women reported the attacks, Lyft did not follow up on their complaints or played down the seriousness of what happened, according to the lawsuit, which was filed on Wednesday in the Superior Court of San Francisco.

“It’s not just the fact that these sexual assaults happened. It’s about the cover-up,” said Michael Bomberger , a San Diego-based lawyer who filed the suit. He filed another lawsuit in September, when 14 women came forward to say they had been sexually assaulted by Lyft drivers.

Mr. Bomberger said many of the women he represents had gone to the police only to learn that Lyft, a San Francisco-based company that competes with Uber for drivers and passengers, had refused to provide information that would have helped investigators.