On-chain addresses don't need an invoice; they can be paid spontaneously.

Lightning doesn't naturally support spontaneous payments, but there are a couple workarounds, including: keysend payments (pay to a node public key), zero-amount invoices (replace the amount with a different number), bolt12 (negotiate via onion messages between nodes),and lightning address (communicate with a server for a specific invoice).

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We created Ghost Payments as part of nostr:npub19tcpurtt6xulhw0r6sc404j9jraj0h8me2lzs7z2tqewz7l0hpas59nlea which enables a central lightning address server for all lightning nodes to use. It's a trusted setup, but enables nodes to receive spontaneous payments without running a separate lightning address server.