How are transactions invalidated by nodes when both parties are offline in a Lightning Network?
AFAIU, if you have open lightning channels, you cannot go offline. You must be online in order to monitor the blockchain for old commitments. If you see an old commitment transaction, you immediately broadcast the punishment transaction, but you cannot do this if you go offline. So if you have open lightning channels, you must be online and if you go offline, you are trusting that the other person in the channel will not attempt to defraud you.