All I can add is I stopped reading your post right here:
the trail breaks when you transfer Munn to Speed via LN because it's happening offline
Neutral feedback isn't that important, and I've never used "Munn" (did you mean Muun Wallet?) or "Speed", but what you wrote here matches the feedback:
This user spread false/fake information on technical board.
I think he meant to send the BTC from Muun wallet to Speed wallet using lightning network. The OP of the thread posted this:
I buy BTC on a KYC exchange and transfer it (on-chain) to a hot wallet on my desktop. From there I transfer it (again on-chain) to Muun wallet on my phone. From Muun I pass it through Lightning network to Speed wallet, also on my phone and finally I send it (on-chain) to my final cold storage address.
According to what I have read about lightning network in the past, it can be used to block the trace, but if someone sent certain amount of bitcoin on-chain to a wallet, open a channel, sent the coin to to another lightning wallet and close the channel on the other wallet, maybe it can be traced if it happened within a short period of time, the amount used to open and close the channel might be used for the tracing, I think. We have seen government trace monero transaction before, I guess it has to do with tracing of the amount and not an error about monero transaction anonymity at all.
I do not know about Speed wallet, I downloaded it, I input one of my useless email but it then asked me of my full name, country and state. I stopped immediately because it might even asked me to get verified but which I do not know about. People should have told the OP on the thread about how such wallet is bad for privacy. I guess it is a custodial wallet entirely. Using wallet like sending from Muun to Phoenix would have been better.
If wallets like Muun, Phoenix, Zeus, Lightning Electrum are used for it and the user does not send the full amount but divided it into different lightning wallets, it will be hard to trace.
@Bitcoin Smith, just settles this with Satofan44 through PM.