It's very easy for someone to come up with an app to order a robotic taxi. This is probably the easiest part of the robotic taxi business.
It's so much so, that unless Uber or Lyft's service is essentially "free," a robotic taxi business will probably consider the cost of working with Uber or Lyft not really worth it and bypass them. They might also prefer the experience of users sticking with their own app in their own walled garden. The robotic taxis will probably have large stickers in them that say something like, "order your next car through us and $AVE!!!" (Just like how JetBlue encourages customers to use jetblue.com)
Or, to be quite honest: If I can actually hail a robotic Tesla taxi next year, I'd rather use Tesla's app instead of Lyft or Uber's app.