What is chainhash, and how can the Lightning Network be considered a "separate network" because of it?
They are different networks in the sense that there cannot be channels which are shared across both blockchains. All channels are based on one blockchain as channels require modification of a transaction for that blockchain. Since Bitcoin and Litecoin use different blockchains, there can only be Bitcoin channels and Litecoin channels.
However, they can also be viewed as the same network because of cross chain atomic swaps. HTLCs allow people to create a channel on Bitcoin and a similar channel on Litecoin which uses HTLCs with the same hashed secrets. This let people atomically swap Bitcoin for Litecoin. So payments can still be routed over this joint network. If someone wanted to be paid in Litecoin over the Lightning Network but you only have Bitcoin channels, you can (in theory, I don't know if this is implemented) route your payment through a node that has both Bitcoin and Litecoin channels using the same HTLC secrets and it would be totally fine. The only caveat is the exchange rate between Bitcoin and Litecoin which would have to be negotiated with that node doing the bridging between Bitcoin and Litecoin.
Good explanation.
It seems that alternative cryptos are helping LN become more secure by widening the breadth of different users and hashrate. Is that a fair assumption ?