I have read that Roberton used the tune associated with a Gaelic song Creag na Ghuanach for the air of Westering Home. Creag na Ghuanach is a portion of a long tale of hunting, by 16th century bard Dòmhnall mac Fhionnlaigh nan Dàn (Donald MacKinlay MacDonald of the poems/lays)
https://calumimaclean.blogspot.com/2013/09/hunter-bard-donald-mackinlay-of-lays.html Òran na Comhachaig (The Song of the Owl)

http://www.bbc.co.uk/alba/oran/people/domhnall_macdhomhnaill_domhnall_mac_fhionnlaigh_nan_dan/

Wikipedia: "The 'Mingulay Boat Song' is a song written by Sir Hugh S. Roberton (1874–1952) in the 1930s. The melody is described in Roberton's 'Songs of the Isles' as a traditional Gaelic tune, probably titled 'Lochaber'.[1] The tune was part of an old Gaelic song, 'Òran na Comhachaig' (the 'Creag Ghuanach' portion); from Brae Lochaber." [Does anyone reading this post have a copy of Songs of the Isles to verify that this attribution is given in Roberton's book?]

Lyrics with translation
CREAG GHUANACH

Air minn o iom ó ro,
Iom ó agus iom ó ro,
Air minn o, na iom ó ro,
Is aoibhinn leam an diugh na chì.
It is joyful I am today to see you.

Creag mo chridh’-sa a’ chreag Ghuanach,
Crag of my heart is Creag Ghuanach
Chreag an d'fhuair mi greis de m’ àrach;
Crag where I received my upbringing;
Creag nan aighean ’s nan damh siùbhlach,
Crag of the wandering deer and stag,
A' chreag ùrail, aighearach eànach.
The flourishing crag of joy and renown.

Creag mo chrìdh’-s a' chreag Ghuanach,
Crag of my heart is Creag Ghuanach
’S ionmhuinn leum an lòn tha fo a ceann;
Dear to me is the pool below its summit;
Is annsa an lag tha air a cùlaibh,
And more dear the cave behind it
Na machair is mùr nan Gall.
Than a pasture or a hall of the Lowlands.

’S truagh an diugh nach beò an fheadhainn,
It is a pity that today the people are no longer living,
Gun ann ach an ceò de ’n bhuidhinn,
Where now only the mist is plentiful,
Leis ’m bu mhiannach glòir nan gadhar,
Who would have had a keen desire for glory with
their hunting dogs
Gun mheoghail, gun òl, gun bhruidhinn.
There is now no joy, no drinking, no conversation.

"Creag Ghuanach is a hill at the south end of Loch Treig where the bard, Donald MacDonald (or Donald son of Finlay of the poems, as he is known in Gaelic) was raised in the sixteenth century. As well as being a poet he was also a renowned hunter. These are only a few verses from a much larger work of more than fifty verses that he composed as his hunting days were coming to an end."
Tom Colquhoun, Largs Gaelic Choir