What happens with the bitcoin locked in the payment channel if both sides lose the backup? If none of the sides closes the channel, is the coin locked up forever?
Tl;dr: also in lightning we have: not your keys, not your coins. 

More detailed explanation:

I assume you mean with backup the private keys of the lightning node together with the history of the state data. 

Then the same would happen as in the onchain case if you loose your keys. You could not move the coins anymore. Or in a onchain 2-2 multisig wallet (remember payment channels are just such a wallet together with some protocol how to spend from it) the same if you and the other person would loose their keys. None of you could move the btc anymore. 

In lightning terminology this would mean that the channel stays open forever but no new states can be negotiated (meaning noone can route through that channel or use it to send / receive payments) and additionally the channel cannot be closed.

While this is a pity for you and your channel partner as in the onchain case it is also a pity for the network as other nodes still think the channel is active and will try to route payments over it.