No because there is no consensus involved: https://bitcoin.stackexchange.com/a/43828/

Although one could say you are staking Bitcoin when you run a node, I'm not sure I'd call it a Proof-Of-Stake system as the term is commonly understood. We're not replacing any consensus mechanism, or voting on anything by having more staked bitcoin. The way I see it, it's a way to facilitate bitcoin-denominated transaction velocity without incurring the on-chain costs. Staking keeps the symbol and the real accounted for.

The LIghtning Network is not generating any coins. It's locking funds between two (or more?) parties (on chain) so they can transact between themselves and settle on chain at a later point.

Proof of work is doing work to win the lottery to get the privilege of furthering the blockchain with the added benefit of allowing the winner to reward themselves with coin.

Proof of stake is staking already generated coin to win the lottery to further the blockchain (and give themselves a reward).

Interesting question. I guess that's based on the premise that large nodes route more? Although true to a certain extent, i.e. very small nodes simply lack the liquidity to open meaningful channels, intermediate nodes are very well able to complete with large nodes, as long as they open useful channels and manage their node well. Now, at the level of the direction the lightning network goes in terms of development, nodes have nothing to say, be it large or small, except maybe in their preference of one implementation over the other. But because all implementations adhere to a global set of rules (BOLT), they are not that different in the end. So no, i don't think the size of your "stake" affects the lightning network.

Thanks for all the answers. For context:

I've been talking about how ridiculous Proof-Of-Stake is for years. When came across the "the Lightning Network is Proof-Of-Stake" idea on Twitter, I felt offended. But I thought about it, and there are definitely some similarities there. It's not exactly Proof-Of-Stake, but... Instead of admitting the idea to myself, I came here to consult with you experts. And thanks to you all, I can keep on saying Proof-Of-Stake is ridiculous!

All's well that ends well.

I might even call it a Proof of Reserves system. In a channel, the reserves are verifiably in the multisig on-chain. 100% of the BTC in LN is backed by these locked funds. This way the terminology of how PoS is used as a consensus mechanism isn't confused with BTC L2 solutions.

maybe Delegated proof of stake (DPoS)?

As it's layer 2, I can't see that it's either POW or POS To say that it's POS is to CONFLATE POS

No.

More stake, more weight?