Yes, micro-payments for online network services is precisely what LN is best at.  

Establishing a channel with each peer is too expensive.   But using LN to micro-pay for high-quality peer services seems like it would aggregate very well.  

It would be great if this protocol was in-place and ready to go in or around the same time LN is ready.   It would incentivize full nodes even further than LN does, and allow the network to be strongly DDOS resistant.