Can the Lightning Network work on any other cryptocurrency? I believe Lightning can be used with other cryptos such as LTC, what needs to be implemented to make it compatible with other cryptos? How difficult is it to implement on those other cryptos if they are compatible?
The answer to this question depends on how broad you define the Lightning Network:


If you want to run the currently specified protocol (and any of the current implementations without having to modify them), you'll need to use either Bitcoin. Litecoin is partially supported by some of the implementations, but Lightning is being built first and foremost for Bitcoin.
If you are talking just about the specification, you'll need to have a Bitcoin derivative that also implements Segregated witnesses.
If you want to port Lightning onto a cryptocurrency, you need to at least support the UTXO model of accounting, and a malleability fix. In addition you need to have some form of knowledge contingent payment similar to HTLCs to perform multi-hop payments.
If you want to drop the UTXO model, you might get away by reworking the functionality in major ways, like the folks at raiden did for Ethereum.


So it's all in the eye of the beholder, but these are the requirements for various forms of payment channels and off-chain payment networks, from simple (and precise) to really hard (and fuzzy).