Yes, Lyft not being YC is is mostly it but also from an early Stripe employee [1]: "Lyft was also not originally on Stripe. They were on Braintree and switched over to Stripe after both Stripe and Balanced (another YC-funded payments company) competed for their business." Balanced was definitely a payments company also backed by YC. I cannot verify the switching from Braintree as I'm mostly an observer in all this but the other details are easily verifiable.

https://twitter.com/cjc/status/1485803509110894596