A paper wallet is not the correct backup method for a lightning network Bitcoin address/channel.
To use a lightning network channel, you will need to have the private keys accessible to your lightning network software, so that the software can sign transactions to update the channel state. So the advantage of 'keeping your keys offline using a paper wallet' is not applicable: if your keys are offline, you cannot engage with the lightning network.
Further, to backup a lightning channel, you need more information than just the keypairs associated with the address, you also need information about the current state of the channel. A paper wallet generally refers to a physical record of a single keypair, so it is not designed to store this sort of channel-state information.
Further still, a lightning channel is represented by a multi-sig address, of which you will likely know only one of two (or more) keys. So printing out your key onto paper will be of very little use in being able to recover your funds later, since you will need the signatures of your counterparty's keys as well, in order to spend the multisig output.
I suppose if you really wanted to, you could print out the static channel backup file onto paper, but without a good way to later transcribe this information back to your computer, it seems like an unwise choice that will be prone to error.
It is advisable to follow the backup methods implemented in the popular lightning network clients, such as
lnd's static channel backups. Here are the relevant commands, from
exportchanbackup Obtain a static channel back up for a selected channels, or all known channels verifychanbackup Verify an existing channel backup restorechanbackup Restore an existing single or multi-channel static channel backup