This can depend. Most car insurance companies work together with Lyft/Uber in order to provide coverage as long as you have a rideshare endorsement.
Below is a break down of how the coverage works. Depending on what stage the accident occurred, you can find coverage from Lyft or Geico.
|Period 0||Offline: Your personal policy|
|Period 1||Online WITHOUT ride request: Rideshare insurance + Lyft coverage|
|Period 2||Online WITH ride request but NO rider:Lyft coverage|
|Period 3||Online WITH rider in vehicle: Lyft coverage|
One of the companies should be covering you via your comprehensive coverage.
You can find more information here.
If they are not wanting to provide coverage, you can seek legal advice to see if you have any other options. Good luck and if you have any questions don't hesitate to ask.