Are you sure?
In the recent book about Uber written by Mike Isaac,the author stated that Lyft was the first to launch a low cost ride service with non professional drivers and Uber rushed to copy them.
Sidecar was the first service I remember that explicitly used the current UberX/Lyft business model when all these companies kicked off in SF. Back then your payment to your Lyft driver was still called a “donation” because it was originally intended as a carpooling app like what WaZe has now.
I read the book last weekend and am going with my memory (I’ve since lent it out). In the book Travis found out about Lyft’s planned rideshare service and raced to launch UberX first.
Alas google has become useless for finding useful information so I hope somebody who still has the book can confirm.