The reason the LSP was able to sweep funds was because what is essentially a bug in Mutiny lead to an invalid, revoked, transaction being signed and published by the Mutiny wallet. This can also be an attempt at fraud, intended to steal money from the LSP. So the Lightning protocol deals with this by allowing the LSP to sweep all the funds, discouraging attempts at fraud.

Harsh. But still self-custodial.

The solution here is to use better wallets that don't have bugs like this. IIUC Mutiny is particularly vulnerable due to bugs in the underlying web browser storage implementation, which can lead to state information not being recorded/modified correctly.