Actually Lightning could use any cryptocurrency in place of bitcoin. Or even multiple cryptocurrencies, with some (or all) nodes and hubs doubling as currency exhanges. That would let users choose the combination of speed, hashpower, and transaction fees that best suits their needs.
That would introduce security issues. There is no evidence that other cryptocurrencies could stand up to the same level of attacks Bitcoin has successfully withstood. If you are using LN, then you wouldn't benefit from the other altcoin transaction specifications anyway.
If a bitcoin channel will cost $20 to set up and close (because of the on-chain transaction fees), while a litecoin channel will cost only $1, I bet that many users would use Litecoin for short-lived connections, in spite of them offering only Litecoin-level securuty.