Is it possible to create pure lightning lockboxes (without touching the blockchain)?

Question

I'm considering a scenario in lightning, where it would be extremely useful to be able to lock the funds in 2/3 lock

Is this possible on lightning network (even in theory)?

Answer 1

I am not sure if I understand your question right. Do you want to have a 2 out of 3 multisig wallet? Theoretically this is very possible. Though practically this will be quite combersome. I guess the best way to achieve this would be to wait for BIP 118 to be activated and then the eltoo upgrade. This would easily enable multiparty channels. This could be used to achieve a scenario as you described.

Answer 2

Every Lightning channel has two participants, funds are initially locked in a 2-of-2 multisig address and each participant has one of the two private keys associated with this address. Threshold schemes like FROST allow you to send funds to the equivalent of say a 2-of-3 with only one aggregated public key going onchain. One of the two (or both) participants in the Lightning channel could use a scheme like FROST to make their single public key associated with the Lightning channel into a 2-of-3 threshold. There are additional keys involved in the operation of Lightning channels once it has been set up but this answers covers incorporating an off-chain threshold scheme into the opening and closing of the Lightning channel.