Does Lightning Network has concept of continuous stream of value?
Streaming payments is not part of the lightning network protocol yet.

However you can build a lightning app that simulates exactly this. There was a demo by alekos Filini on lädt years lightning residency. Check out https://youtu.be/IlSVTir_9Ns

When AMP is coming streaming payments could be stimulated with AMP by setting up more and more routes. But that would be rather fancy. 

So I guess you create an app on top of lightning to solve streaming payments