Thanks to discussion on this forum, I realised that it wouldn't be too hard to hack together a mail-only "server" for LSN. So I did that. It's currently running on my machine, and I'm hereby opening for public use.
Probably there are lots of bugs; I'm hoping people will test it by playing some games.
In short - you start a game against someone by sending a mail to the server specifying your opponent's email address; turn files get mailed to you and your opponent by the server, which you can open in your LSN client. You mail your orders back to the server. With a little hackery, you can get the client to do that for you - see USAGE for details.
So it works much like the original server, but with no web server, no dedicated SMTP server, and no leagues etc.
I'd be pleased to accept games - my address is [email protected]
Hopefully people will find this useful, but I should make it clear that this is only a temporary, better-than-nothing solution, and isn't really a replacement for an official server. If anyone has access to an always-on linux server, we could get much closer...
I hope setting up this server won't be controversial. I did contact codogames to give them a chance to tell me not to, but they didn't reply.
The core of the system is the bash script lsnautomaton.sh which automates the method suggested by Warchief and Jaques Cartier on these forums for keeping a hotseat game going and getting it back to the point it was at if it dies. So thanks to them. This script, or the tricks it uses, might be useful for other purposes.