Lyft is barely in any locations compared to Uber which is everywhere. If Lyft expands to way more countries then maybe.
Lyft's current tremendous expansion is literally fueled by Uber's astonishingly bad PR and management. Drivers and their cars as it turns out, can move easily from one to the other.
Uber's attempt to destroy Lyft has backfired with the blazing pyrotechnic spectacle of a gaf sex advice thread.