An LN payment processor is not institution, it's just a LN node which has channels open to many other nodes and to which you as a user can connect to, so you don't need to open separate channels with everyone you are doing transactions with. And if your LN node becomes unreachable due to censoring: they are often available over Tor too.
It doesn’t need a lot of BTC tied up in channels. It’s enough to have one channel open with another well connected node. Transactions can jump over several nodes to reach their destinations. And everybody can become a bank/payment processor for their friends and family with an LN node, no need for big centralized institutions.
We were talking about the well connected nodes, they need funds tied up in many channels. That's what makes them well connected. And effectively institutions. If it takes off don't be surprised if such entities start charging fees.
It's up to each node how many channels they open and how much bitcoin is used for those channels, but lots of channels doesn't make it an institution. An LN node has to play with the same rules as every other node, it cannot enforce rules like institutions. And if you don't like some LN node's transaction fees, you choose a different node for your transaction to go through. As a result the high-transaction-fee node will soon lower its fees. Btw, every LN node is already charging fees.
