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for a public one, must be bigger than 3M-5M sats at least.
It must be a hassle for node operators to rebalance channel liquidity when large amounts are constantly being moved, tho
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I think there are apps for this... that balance channels/manage liquidity automatically.
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Yes you can.
Rene Pickhardt demonstrate how he sent 1 BTC over LN .
Here is his YT channel with more demo videos
https://www.youtube.com/user/renepickhardt/videos
Over LN you can literally stream payments. The only restriction is the size of the channels on the path. If you can find enough liquidity, you can send 1 BTC easily.
https://bitcoinmagazine.com/technical/pickhardt-payments-how-to-send-large-bitcoin-payments-on-lightning.
My personal biggest payment over LN was 5M sats, using 2 hops. But for example you could very easily send 5 payments of 1M each over the same route.
Why smaller amounts is better? because sometimes the routes are limiting the max HTLC to avoid fast drainage of the channels.
I am not worried about the limitations imposed by nodes, but by people not using LN and opening big channels. I still see people opening tiny shity channels of 100ks sats, with public nodes ! Maybe for a private mobile node is OK a 100k sats channel, but for a public one, must be bigger than 3M-5M sats at least.
Imagine a pipeline struggling to send large volume of water through tiny pipes....
Very good question btw.