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In his recent talk, Andreas Antonopoulos said "By probably the end of 2016, Bitcoin will have a hybrid proof-of-work/proof-of-stake system." and then continues to label the Lightning network as a POS system.
Is the Lightning network a proof-of-stake system?
Calling the Lightning Network (LN) a Proof-of-Stake (PoS) system is orthogonal to the concept usually labeled as PoS.
What we usually describe as PoS is a mechanism to achieve distributed consensus among a network of participants. Staking is hereby providing updates to the whole network's state, by which participants earn fees for contributing to the validity and the security of the network.
On the other hand, there is no global consensus in the LN. The LN is a system of bilateral smart-contracts, where you may earn a fee by providing liquidity to other users. Nodes along a payment path forward payments, but even these contracts are created, verified, and executed between a small number of participants. Conflict resolution is achieved by publishing on-chain transactions which indirectly leverages the proof-of-work of the Bitcoin network. While nodes announce themselves and their channels to their peers, there is no datum on which the whole LN must agree.
In fact, not even the two channel owners locally run a consensus protocol. If one side proposes an HTLC, the other side can accept or decline it. When the channel owners disagree on something, e.g. feerates, or collaboration breaks down in another manner, the process breaks down. They will not reconcile, but shut down the channel and disconnect rather than converging on a shared state.
Let me disagree with the one asking the question and answering it, the Lighting Network is using PoS, the network connects nodes by channels that are created using a transaction on chain (the funding transaction), no LN connection is possible without it, this transaction is the stake.
Also, the strength of the connection is given by the bitcoin blocked on the funding transaction, limiting the volume that can be transacted on that channel.
That make a clear PoS based network.
What @Murch is pointing is that it: "is orthogonal to the concept usually labeled as PoS." and I partially agree with that, given that the term "PoS" is very commonly used for blockchain consensus, and as he mentions "there is no global consensus in the LN".
But, while there is no global consensus on the LN, there are local consensus on each channel, and also on all the channels involved on each transaction (the payment path), so there are many local consensus and those are based on a PoS.
