algorithm thinks I 'let time run out'

Warning, ***. Letting time run out instead of resigning will result in a temporary ban.

But I didn't-- was playing 2-1, trying to figure out a way to survive, playing moves, and timed out while looking for a way to escape. Very tactical position. Probably thought for 6 seconds before timing out.

Maybe you could allow both players to comment whether they thought there was abuse. If both players deny abuse, you could adjust the warning algorithm.

Sometimes I disconnect and lose on time, and it says that "Letting time run out instead of resigning will result in a temporary ban."

I don't get why, I'm pretty sure that Lichess can recognize when I disconnect.

I wouldn't worry too much about this warning. If you don't do this often then you will be fine. But if you do this all the time, you will get in trouble.

Well it's definitely a bug if 6 seconds triggers it.