Calling Lightning a Proof-of-Stake system is orthogonal to the concept usually labeled as PoS. Him having done so will just generate loads of confusion.
What we usually describe as PoS is a mechanism to achieve distributed consensus among a network of participants. Staking there is providing updates to the whole network's state, where you earn fees for contributing to the validity and the security of the network.
On the other hand, Lightning Network is a system of bilateral smartcontracts, where you may earn a fee by providing liquidity to other users. Nodes along a payment path don't provide any proof whatsoever, they merely forward a payment. There is no global consensus in Lightning, contracts are created, verified, and executed between two or a small number of participants. Any need to create consensus in the case of disagreement is provided by the proof-of-work of the Bitcoin network.
I could see the LN as being considered a kind of proof-of-stake network, only insomuch as nodes with large amounts of bitcoin tied up in their channels will be more likely to be used as central hubs and for larger transactions. Still, this is vastly different from other proposed and implemented proof-of-stake systems. – Jestin – 2016-04-25T18:59:24.753
@Jestin: There is stake involved, but where is the "proof" part? – Murch – 2016-04-29T09:06:37.743
I don't think there is any proof. It's more like a network effect, where those who have the most bitcoin to lock up in various channels will eventually become the central hubs of the network, and therefore earn the most fees. The decentralized control comes from the Bitcoin network, itself, not the overlay that is the LN. Your stake invested into your channels doesn't really give you any more control of the network than anyone else. For example, a majority stake holder could not prevent a transaction from going through, since it could be routed to bypass that stakeholder's nodes. – Jestin – 2016-04-29T13:27:07.777
@Jestin: Agreed. (Continuing to be the devil's advocate here:) It's not a consensus system, there is no proving involved. Why would you then call it "a kind of proof-of-stake"? – Murch – 2016-04-29T13:54:12.427
A pure proof-of-stake network has proven to be hard to implement, and many of the attempts/proposals are hybrid with some other form of consensus or trust. I can see AA's point how the LN might not be so different, since a larger stake gives you an advantage in the network...but I also don't really agree with him. The larger stake gives competitive advantage, but not any power of control. Stake plays a role, but not the same role as is played by hashing in Bitcoin. However, since none of the other PoS proposals I'm aware of rely 100% on stake, I can see why AA made the connection. – Jestin – 2016-04-29T14:17:32.103