If you are able to receive PIP benefits, then no, as no-fault laws which require PIP benefits will limit the right to sue. In cases where you cannot receive PIP benefits, then you have the right to sue if the Uber or Lyft driver is at fault. If another driver is at fault, you may sue them instead. Additionally, New York law requires ridesharing companies to provide varying amounts of uninsured and underinsured motorist insurance depending upon circumstances, which would cover the costs associated with any injuries the at-fault driver couldn’t pay for.