LND specific answer

Basically the server has this identityKeyLoc property: https://github.com/lightningnetwork/lnd/blob/9c97d26cfb505081732cb457b513a356879ad57e/server.go#L160

that is used whenever your node announces itself to the network: https://github.com/lightningnetwork/lnd/blob/9c97d26cfb505081732cb457b513a356879ad57e/server.go#L2766

According to this comment here about key locators https://github.com/lightningnetwork/lnd/blob/7106ea59db9ade78d65bb46605f94637900c0e3f/keychain/derivation.go#L140

It seems to generate ECDSA public keys using a BIP43 like keychain system commonly used for wallets.

So ultimately it is derived from a BIP43 like key derivation mechanism based on the comments. Like what you would see in a wallet.

I don't think there would be anything stopping you from modifying this and just hardcoding a custom vanity key.

Or somehow generating a path/keyindex that derives your vanity key.

However, most node public keys are commonly displayed in base16 so you don't have a ton of options other than making a vanity like DEADBEEF1234567890...

Given the limitation, I'm not sure if that would be worth doing. Probably better to just define yourself through an alias.