Tarsnap's revenue is all the picodollars users spend, even though I pass quadrillions of them over to Amazon to pay for the storage I'm reselling. But Amazon is definitely not my employee.
I'm not trying to answer the "contractor vs. employee" question. There are many factors which go into that determination and I don't know enough about Lyft to offer an informed opinion about that.
My point is just that a contract between you and Lyft which states that Lyft will get someone to drive you somewhere does not imply that Lyft's drivers are employees, because the presence of a contract between Lyft and its customers is entirely consistent with Lyft's drivers being contractors.