"We lost him" is used in the sense you mention and of course it doesn't mean that the disconnected person died, but precisely that the connection was lost.
Not always "we lost him" means he died, there are several meanings depending on context.
It can mean literally that you were following him and you are not able to see him anymore: "General, we lost him!"
Or that you were talking to him on the phone or videocall and you are not able to do so anymore, as in your original example.
Or that you were giving an explanation or talking to him and he stopped paying attention: "Stop talking, I'm sure we lost him when you started talking about the complex derivative of the swaps."
I'd say the common thread is that you had a tie with a person which is what's lost. Which tie, depends on the context.