Lordran is the kingdom in which Dark Souls, and therefore the player's journey takes place. It encompasses all of the traversable areas in-game.
The Undead Asylum is potentially outside of Lordran, to the North, according to the cinematic intro:
The Darksign brands the Undead.
And in this land,
The undead are corralled and led to the North,
Where they are locked away, to await the end of the world.
Only, in the ancient legends it is stated,
that one day an undead shall be chosen to leave the undead asylum,
in pilgrimage, to the land of ancient lords,