Congrats 🥳
You kind of solved the problem for 0.01% of users that will do that.

Now here are the other privacy problems that come with LN, that Monero doesn't have, for the 0.01% of those users:
-Receivers have notoriously bad privacy
-Amounts can be probed by a large routing node
-Data gleaned from onchain footprint used to open/close channels(including name of node you opened/closed the channel to/from)
-Any effectiveness of onion routing is reduced/nullified if most of the network is using large centralized nodes to transact (which is incentivized for successful routing and cheapest fees)

Here are general LN problems (that neither Bitcoin nor Monero have):
-can't send larger amounts
-need to have sufficiently funded channels to use
-can't receive offline
-requires a hot wallet to receive
-can be rugged if your node is offline
-can be force closed against your will

Here are the problems specific to Phoenix:
-Centralized servers in France
-They calculate routes for you so know amounts and destinations
-They allow you to receive by being a middle man so permissioned
-You pay them extra to transact
-If they go offline, your wallet is useless
https://phoenix.acinq.co/privacy
https://phoenix.acinq.co/faq#how-private-are-my-payments-on-phoenix

There is a reason no one uses the Lightning Network on Darknet Markets.


Here are some people you may know talking about the state of lightning privacy:

"Lightning right now is a privacy nightmare" -Giacomo
https://youtu.be/P1PRKKlI-Jo?si=OXtZUHPiBmanbNuC&t=1691

LN devs telling you its not private:
bitcoinmagazine.com/technical/state-of-bitcoin-lightning-network-privacy
https://abytesjourney.com/lightning-privacy/


"We identified 27,183 private channels, discovered hidden balances, and showed how a passive adversary can infer payment endpoints with very high probability."
https://arxiv.org/pdf/2003.12470.pdf