As LSN is a windows game, you will need an emulator. The easier / cheaper i found was winebottler, an overlay of wine.
1. Download and install winebottler : http://winebottler.kronenberg.org/
2. Get the LSN client installer (will1k provided it there https://www.dropbox.com/s...a093jl64urx1h/UAOoLlj-oI )
3. Open winebottler (from the Applications folder), select "create custom prefixes", select the LSN installer file, then in winetricks you will have to check directx9 and sdl - you may have to try some other combinations upon your config, i used also vd=1024x768). Proceed through the install. At the end, wine will ask you which exe will be opened when you double-click the pseudo-mac app, be sure to select the LSN game).
4. double-clicking the new app should launch the game. Opening .lsn resultats file with it should work.
5. To send turns, select "save file". The orders file won't be in the packaged app, but in your home Library/Application Support/Wine folder.