This pre-dates nostr and never really caught on: https://github.com/squeaknode/squeaknode
If the node supports keysend, you can send a message attached to a payment. https://docs.lightning.engineering/lightning-network-tools/lnd/send-messages-with-keysend
Thunderhub let's you read any keysend messages you've received.
LN isn't supposed to be a social network. The existing platforms work great for communicating with node operators.
Claim your node on Amboss by signing a message, then you can tag your node with the various communities you want to associate with. For example: https://amboss.space/community/6d41c0bd-6e39-40a2-a062-a809c2e8c2b5
You can also verify your twitter and add other contact details to your Amboss page: https://amboss.space/node/024bfaf0cabe7f874fd33ebf7c6f4e5385971fc504ef3f492432e9e3ec77e1b5cf
Could put any nostr address up there. I don't see why your node needs to sign anything to claim an address, just make one and share it!
The need to claim the address was so we can know in advance what is the address to contact any node, thus being able to contact any operator without them having to advertise their contact address. But then obviously you wouldn't know if a node operator has claimed it or will ever see your message
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