I can't help with the chords/music either, but there is a very nice recording of a different version of this song (titled "Lassie Lie Near Me") recorded by Dick Gaughan on the rather rare "Folk Friends 2" album. The lyrics are very different from either the one above or the very similar one in the DT, but it's still recognisably the same song structure and presumably the same tune.

Dick's version is from Hogg's "Jacobite Relics", Vol. II and it specifically mentions Culloden. The best shot I can make at transcribing the Scots lyrics is (with a fair dose of interpolation):

Long hae we parted been, lassie my dearie,
Noo we are met again, lassie my dearie.
Near me, near me, lassie my dearie,
long hast thou lain alane, lassie lie near me.

Frae dread Culloden field, bloody and dreary,
Mourning my country's fate, lame me(?) and weary.
Weary, weary, lame me and weary,
They(?) come as a banished weight(?), far frae my dearie.

Loud, loud the wind it roared, stormy and eerie,
Far frae my native shore, danger stood near me.
Near me, near me, danger stood near me,
Noo I've escaped the moor, lassie lie near me.

All that I hae endured, lassie my dearie,
hearing (thy name's ae cure(?)), lassie lie near me.
Near me, near me, lassie my dearie,
^^