Are several serial numbers needed to play on LAN ?
In what game? Earth2160? Yes, you need to obtain unique serial number as game recognize itself by this number. If you'll try to launch multiplayer mode (not earth.net) then game might report error saying that serial number is invalid. For earth.net play you need additionally activate/register your copy with earth.net servers.
i wonder if the trick here http://www.gog.com/en/forum/earth_series/q_amp_amp_a_serial_request_at_launch
will work by just changing the number "manually", since i don't believe that the executable will fully validate (with its validation algorithm that you normally encounter when entering the serial code) the code, and just check if its the same or not.
but i have to test that later
WELL that didn't worked out, seems the game checks for the validity of the serial right at startup of the main executable, so i have to keep within the validation algorithm - no biggie for me, done that 4 years ago ;)