Neither The Lord of the Rings: The Battle for Middle-earth (2004) nor BFME II (2006) supports **local network (LAN) multiplayer** — with one exception.
lotrbfme2.exe inbound/outboundNote: BFME I cannot do LAN even with patches. Community uses virtual LAN (Radmin VPN, ZeroTier) + modified launchers to simulate LAN over internet for both games.
If you want LAN RTS in Middle-earth: BFME II 1.06 only. Otherwise, use community online revival.