Lightning wallets sometimes have a feature where you can sign a message. Ride the Lightning (RTL) and ThunderHub can do it, not sure which others.

When a site has log-in-with-Lightning, they give you a message to sign. You paste it into your wallet, sign, then copy the result. Lastly, paste the signed message back into the site’s field for that.

This allows you to prove that you control some Lightning node. Sites like Amboss use this to let you add info about your node. Lightningnetwork.plus lets you log in that way to participate in liquidity swaps.