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.
Alas google has become useless for finding useful information so I hope somebody who still has the book can confirm.
As others said, Sidecar was technically the first to the "ridesharing" model
Zimride (lyft) started the first rideshare site. Unless you count craigslist ads.