The only way to use "offline" LAN Multiplayer is only if you have the original Gold Edition of the game or any of it's critical files, such as the AvP.exe file.
And even then, you would still need a wrapper program such as dgvoodoo2 for this to work.
Why? Because AvP Classic 2000 had the local multiplayer options from the original "Gold Edition" of the game such as TCP/IP removed altogether. It's unfortunate and they just never seemed to got around restoring a local offline multiplayer mode.
So if any of you still have your Gold Edition CDs it's easier to restore LAN Multiplayer than you think it is. But if you don't have it, you may have to look for someone that has it and is willing to share some of the files on the original discs and get dgvoodoo2 to run AvP Gold to play LAN Multiplayer.