99% of LN liquidity pools is controlled by CEX and other custodial liquidity providers.
It's that easy. All of them join with a money transmitter licence that means sharing data with chainanalytic companies.
In that regard Tor is vastly different from the LN. Both are theoretically passively surveillabkr, but due to the centralisation effects (liquidity for routing), LN loses a lot of the properties and while Tor is more of an egalitarian network opening channels is a social selection process.