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Partly, but the key distinction is custody. A bank holds your money; an LSP (in self-custodial setups like Phoenix/Breez) opens a channel where you hold your own keys and can force-close to chain unilaterally. What the LSP can do: see your payment graph edges (your counterparty is usually the LSP, so it sees amounts/timing; with trampoline or blinded paths it sees less), refuse service, and set liquidity fees. What it can't do: spend or freeze your balance without your signature.
So the realistic risk is less "bank" and more "chokepoint ISP": KYC rules could be imposed on large LSPs, and users would face onchain fees to exit. Mitigations being worked on: splicing, multiple LSPs per wallet, LSPS open specs (interchangeable LSP APIs), and Ark/channel factories to cut onchain cost. Uncertain part: whether exit costs stay low enough during fee spikes for the "you can always leave" guarantee to be practical for small balances — for a few thousand sats, it often isn't today.