I don't know the answers to this strange question. What's the most you can send to another bank account without compliance issues?
> But companies and organizations routinely transfer millions and billions between normal banks
Just like companies have direct lightning channels between each other, they can send billions of they please.
Note that not all channels are public, so you won't find all in searches. I'm only saying that you shouldn't be worried about lightning liquidity if you can directly connect to your counterparty - as you can directly transact with that party without relying on any liquidity from anyone else.