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