Pretty simple: Do I really need to buy another copy of NWN2 in order to play Storm of Zehir on local Lan?

Most Likely:

To play any kind of multiplayer, NWN checks for a unique key.

Check you account under the game, under more, under "Serial Keys".

So you would need 2 copies , to have 2 sets of unique keys to play multiplayer Coop at home.

But:

There is a small chance you might be able to do it with one key.

The game actually installs with a default install key that is the same for everyone, so you can't play online with this as you would run into many with the same key. There is a small chance that this key still works as a key and maybe allow home with two players.

Install one copy with default key, and one copy with your multiplayer key and give it a shot. I only have one computer at home so I can't test this.