This is a fun thought experiment.

Here’s how I would do it:

Set up a basic node with Core and LND/CLN. Umbrel is probably fine for this, the truly paranoid would roll their own setup (raspiblitz etc.)

Connect it over a VPN so your traffic is private from your ISP.

Source KYC free onchain funds to add to your node wallet.

Open a private channel to a well connected routing node over Tor.

For ease of everyday use, connect a good mobile wallet to your node. Zeus is good and doesn’t have in-app analytics or trackers.

Loop a portion of funds out over Boltz to get some inbound liquidity and balance the channel.

Consider opening 1-2 more channels for stability, but 1 will probably work if it’s a decent a node.

Biggest privacy leak in lightning currently is receiving funds, as invoices encode the pub key of the receiving node. So consider using LNproxy for receiving Lightning payments (receiving for your use case is probably just buying sats to top up your wallet, RoboSats is great for this).

Start spending!