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). 

 We created Ghost Payments as part of @Amboss 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.