The Xbox 360 version of The Lord of the Rings: The Battle for Middle-earth II does not include a Skirmish mode. This feature—custom matches against AI with selectable factions, maps, starting resources, and victory conditions—was exclusive to the PC version.
Console RTS controls (gamepad) made the complex Skirmish UI (faction select, map settings, AI difficulty sliders, team configuration) difficult to navigate. EA opted to streamline for the console audience.
Play the PC version (available on Steam/Origin, runs well on modern hardware). It supports mods, higher resolution, full Skirmish, and the Rise of the Witch-king expansion (not on 360).