I've only ever heard Martin's rather fine tune used (it is his own), though it's a well-known poem and there may be other settings.  I don't see any reference to death in the verses, and have always rather imagined a reference to Byron's notorious (alleged) incestuous relationship with his half-sister, Augusta Leigh; certainly the poem is particularly poignant if read in that light.   It's not even slightly Irish; Byron was English of Scottish descent, and Martin is English, though he spent quite a time working in Australia and specialises in the music of that country.

Malcolm