How will this be handled in a dispute? receiving
sending the payment for that content>

You can wait until the channels close (they eventually will, and maybe even faster than their expiration date), and then you'll see your transaction broadcasted on the blockchain, since it's the only way for them to get your funds.
Or in the case of "pay-per-minute streaming content", you stop streaming to them and ban the peer if they don't send the micropayment in time.