No, you may not be calling their API endpoints directly with HTTPS requests initiated from your own code. However, as I understand it, you're effectively pushing the buttons (or hooking the methods, idk android) within the Uber/lyft app, which causes their app to call the API endpoint. So you are certainly calling the API, just indirectly. Regardless, your app is definitely "automating usage" of the Uber/lyft app, and could therefore be in breach of their terms of service.

I'm not arguing that there are no workarounds or hacks or backup plans to whatever technical obstacles Uber/lyft may throw at you. In fact I'm quite familiar with them from the iOS side. However, as a high profile startup and US corporation (funded by YC), you can't blatantly ignore a C&D just because you disagree with it. And you definitely can't introduce new hacks or workarounds after receiving the C&D. Your only option would be to fight it in court.

(Also consider the play store / App Store can remove you at any time without any legal due process, and will likely do so when notified of noncompliance of a C&D)

Don't get me wrong, I think a court battle over this kind of client-side integration is sorely needed. But as an investor, I would be concerned my money would end up in a lawsuit before the app even gets traction. If you're planning on a lawsuit, you might actually win it.

Incidentally, if you're taking the attitude of circumvention, then you could "go all the way" by asking users to sideload (via 7 day developer certs) a custom version of the Uber/lyft apps that includes code to interface with your app. That's the approach I took to automating iOS apps in the past, but that was on jailbroken devices. Side loading presents a hard usability problem, but I bet you could convince users to plug their phone into their computer every 7 days.