Here's how you pay tiny amounts of bitcoin; using a Cashu Spilman Channel. It could be used to pay Nostr relays for each request.

This sets up a Cashu Spilman Channel, in a demo system using a channel to pay a Blossom Server for the video segments being served.

The client (the video player) and the server (the video server) need to trust the mint, but they don't need to trust each other

The client creates a funding token, and then each payment is made simply by signing a Cashu "swap" which releases more of the funding token to the service provider (the video server). The two parties can sign and verify transactions locally, without needing any communication with the mint, thereby allowing very high frequency payments

https://youtu.be/BwKAe8x7BR8