If you use the Breez SDK, you can do this, I did this with Agora. But technically it's not perfect because Breez could ban the app API key. Though users could take their seed words elsewhere and get their funds.
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If a new person signs up for Nostr…
Generates a pub/private key pair …
Creates “an account “
With a profile pic and a bio and stuff …
Why can they not just automatically get a 12 word seed phrase to a non kyc built in wallet like Zeus or something ?
Could you build a Nostr app like that where when a new user signs up for Nostr they automatically are onboarded to a built in Zeus wallet in the Nostr app and can start receiving and sending zaps ⚡️ instantly using ecash???
Then when their balance gets big enough to open a lightning channel it automatically does it for them
And so in their settings they could see their public/ private Nostr keys and their self custody non kyc 12 words to the built in lightning ⚡️ wallet??
The issue currently with the Breez SDK is that it is a one-way street to centralization and surveillance by LightSpark, which I don't think anyone wants. You can review my whinging on this issue here: 
GitHub
No clear way to run an SSP without a business relationship with LightSpark? · Issue #64 · buildonspark/spark
This project seems to be gaining momentum and there are community concerns that both SSPs (lightspark, flashnet) are controlled by the same family....