[SimonPStevens]

Segregated witness is nothing to do with off chain transactions. SegWit just moves some signatures around in the block so more transactions can be fitted in each block.

This does have some benefits for off chain transaction networks because it changes what parts of the block are signed and need to be verified. Off chain transaction networks can still work fine with or without segwit though.

[sowbug]

It is related in that it addresses transaction malleability. It is not the only possible solution to that problem.