After being shot, the driver lost control and sheared a hydrant.
The shooting happened just before 5 a.m. Sunday near Eagle Rock Boulevard and Avenue 40 in the Glassell Park area just north of downtown LA.
Police say the driver had two passengers inside the car, but they were both OK.
The driver is in critical condition.
Investigators are now trying to figure out if road rage is to blame.
No one has been arrested and so far, there's no description of the shooter or suspect vehicle.
Lyft issued a statement reading in part: "These allegations are extremely frightening and upsetting. The safety of our community has been our number one priority since day one. Our thoughts are with the driver, who we have reached out to to extend our full support."