You're not private from your custodian at all if using custodial lightning.
You're not private to state level intelligence what has control of BGP traffic and can monitor multiple hops and perform timing analysis no matter if you're custodial or self custodial.
If custodial you're not private from your channel peer since you link a UTXO to your entire channels activity. This is less of an issue if you're perfect about UTXO hygiene and connect to the peer over an onion connection.
The only exception here is ECash which has incredible privacy but is highly susceptible to counterparty custodial risk of the mint.
Monero? Private by default both to state level network monitoring AND chainalysis. You can't mess up UTXO management or accidentally connect to an Electrum server with your KYCd IP doxxing your UTXOs past, present and future.
I'm curious how long it'll take for this charade of yours to go on. You bring this up very frequently now I give it a few more months.