This is very interesting: if you could operate your side of a lightning channel as a multisig, could you make it safer? I think a threshold of signers would all have to stay online, but compromising your node would now require compromising a threshold of signers.

thresholdizing a Lightning party requires nesting a threshold signature scheme inside of an established two-party MuSig2 protocol without altering its nonce exchange or message flow.

In this work, we resolve this limitation by formalizing nested threshold multi-signatures, a new cryptographic primitive for thresholdizing one participant inside a multi-signature protocol.
As an instance of this primitive, we present Iceberg, the first construction for nested threshold MuSig2 signatures.

Iceberg enables one side of a Lightning channel to operate as a -of- threshold group while appearing to the counterparty as a standard MuSig2 participant.

As a result, threshold custody can be deployed unilaterally on today's Lightning Network without requiring any modifications to Bitcoin, the Lightning protocol, or channel counterparties.

Our measurements show that thresholdizing a Lightning channel incurs only modest overhead, since a threshold group tolerating one corrupted member sustains over of the payment throughput of an unmodified endpoint.

It does seem like added complexity, though. And lightning already does have a bit of complexity.