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.