So yes, the Lighting Network absolutely is a set of rules built on top of Bitcoin's blockchain AND Litecoin's blockchain AND Vertcoin's blockchain, etc.
but you and your chums love to define it as a purely bitcoin feature and a layer of bitcoin. rather than a separate network used for multiple cryptos
the differnce in the wording is about how much hype and stuff..
The reason people primarily talk about it as a Bitcoin feature is due to network effects. In the past, you've made repeated comments about Lightning's success being dependent on actually being able to route a payment. If you now want to undermine that argument by claiming that you can get exactly the same benefit using LN on Vertcoin where there's comparatively a pittance of channels to route through, then go right ahead. But I think even a diehard detractor like you would be forced to admit it's going to be easier to route a payment on Bitcoin's LN network than it is on Vertcoin's.
LN on Bitcoin is the one most people are using.