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But if the LSP is able to sweep your funds then it clearly is not actually self custodial.
This is how all lightning works, and is not specific to Mutiny, LDK, or any other lightning node software. If you run two copies of your lightning node, one is behind, and that one that is behind force-closes, you will lose your funds. Sadly iOS-PWA has a bug which has been causing that for Mutiny, but they've been working with their LSP to send users their funds back in that case.