The Lass of Aughrim is a fragment of a ballad called among other things, Lord Gregory, or the Lass of Rough Royal, or Fair Annie of Lochroyan. Child 76.

The Dead is actually a short story by James Joyce, which John Houston adapted into a film. The Lass of Aughrim appears in both. I won't spoil your enjoyment but the song is one of several motifs which appear in the story as part of Joyce's critique of Irish (Gaelic) nationalism.