Are you worried about a cease and desist from uber/lyft for building a "third party client" that interfaces with what is effectively a private API? There is plenty of precedent for them to send you a C&D for that, as many companies do with third party apps (e.g. Snapchat is very aggressive). Beyond that, won't it be a constant cat and mouse game of making sure your app integrates with uber/lyft?
It's very telling that you don't have an iOS app, likely because the security model prevents this kind of integration hack without jail breaking, or if you're lucky, some creative use of URL schemes.
I know you say you're "helping user churn" for uber/lyft, but those companies are certainly not obliged to agree with you and can send you a C&D at any time (I would bet on it). I can't see how you can build a viable long term business on a hack like this, where you are effectively an unauthorized third party app subject to the whims and possibly lawsuits of uber/lyft.
If you get a C&D from either Uber or Lyft, your product and business model no longer work, unless you're willing to go to court or blatantly ignore the C&D and the law by circumventing any technical measures introduced to stop third party apps.
No offense, but I'm honestly surprised YC funded a company with such a fragile basis of operation. Unless the plan is to go to court and fight any C&D, in which case I'm certainly rooting for you to set a nice precedent for third party apps.
Overall though, it's a great business idea and solid MVP. Good luck and boola boola.