The first statement is interesting because it renders all others irrelevant, if LN is not a blockchain, which is true, how is it auditable? Doesn't the emission and usage of the LN "kills" the trust of BTC as its "famous" supply limit?
When you realize that no one really understands LN privacy and that they are also incapable of understanding network-level privacy, you realize that no one in this space really has a clue about privacy, except for nostr:nprofile1qythwumn8ghj7ct5d3shxtnwdaehgu3wd3skuep0qyt8wumn8ghj7etyv4hzumn0wd68ytnvv9hxgtcqyqsc8628tpyp6rcjf77e83tve2j9ulj5tnht34fgfrucy5l5j7uh2r2aejt
- LN is not a blockchain, and since it uses routing like Tor, in most cases it will always be more private than any blockchain, even Monero, simply because LN does not leave public records for later analysis and all information is encrypted, including the amount and routing fee, in the same way as Tor.
- For the recipient, simply use Blinded Paths or LNproxy. You can also combine them in case a client is not compatible with Blinded Paths.
- It's also useless if you use LN, Coinjoin, or Monero and don't protect your privacy at the network level. Your LN node must be behind Tor, and if you use services like LNProxy, do so behind Tor as well.
Discussion
It is not auditable but cannot increase supply of the base layer because payment channels open and close on chain so a channel can't close with more sats than it opened with, just a different split between the two parties in the channel.