I really tried to understand what you were trying to ask but i'll answer as I understood it.
LAN and Online gameplay are 2 different things. For LAN, you and your friend need to be on the same network, probably in the same room or building connected through some LAN settings. For this, you do not need internet.
If you both wish to play from your own houses, then you will have to check out Online Multiplayer if that option exists in the game. You will need Internet for this and doesn't depend on your LAN settings.
This is the case for almost all games that support multiplayer option.
Hope you got what you came for.
