(i) The first is a zombie attack, where a set of k nodes become unresponsive with the goal of locking the funds of many channels for a period of time longer than what the LN protocol dictates.

(ii) The second is a mass double-spend attack, where a set of k nodes attempt to steal funds by submitting many closing transactions that settle channels using expired protocol states; this causes many honest nodes to have to quickly respond by submitting invalidating transactions.