How do the privacy mechanisms of Monero (ringsig, ringct & stealth addresses) affect the implementation of a second layer, like the lightning network?

Question

I can make sense of how the Lightning Network is implemented in Bitcoin, and why SegWit was a big deal for it. Fluffypony talked about implementing LN in Monero, so I am wondering how the privacy features (and lack of SegWit) complicates the solution.