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.