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.