Most of it was straightforward enough, but what pronunciation did Burns have in mind when he wrote Luve? All you hear today is /lʌv/, but if Burns had intended the same pronunciation as in English, he would surely have written Love instead.
Fortunately the SND has a very helpful etymological note:
[O.Sc. lufe, luff, 1375, love, 1450, O.E. lufu, love, lufian, to love. The reg. development in Sc. through North. Mid.Eng. lōve(n) is [lø:(v), ne.Sc. li:(v). See O, letter.], attested by J. Elphinston Propriety (1787) II. 200 (“u French”), W. Aiton Agric. Ayr. (1811) 688 (“Greek upsilon”), J. A. H. Murray D.S.C.S. (1873) 147 and the spelling lee, but the mod. unrounded forms of these [lɪv, lev] have been wholly replaced by Eng. [lʌv]. The 18th c. spelling with oo adopted by Ramsay and others has misled singers and reciters into the now common pronunciation [lu:], the word having dropped out of colloq. use.]
What this means is that Burns probably pronounced Luve as /le:(v)/ (there’s evidence for the unrounding of /ø/ in his pronunciation in rhymes such as ane /jɪn/ — abuin /əbɪn/, not /əbøn/), but that this pronunciation died out a while ago.
In effect modern Scottish love is thus a borrowing from English, and this has fully replaced the native word.
If anyone wants to revive the auld Scots word (or just wants to pronounce it correctly in older poetry), there’s thus a choice between luiv(e) and lae (not *lui: <ui> is never used word-finally — we write dae and shae, not *dui and *shui in spite of the vowel being the same as the one in puir and shuir), with the expected pronunciations (/le:(v)/ in Central Scots, /li:(v)/ in Northern, /lø:(v)/ in Insular).
I can’t help wondering whether /le:/ died out because it became homophonous with ‘lay’ in the Central dialects, which might for instance have added a potential new meaning to the line And I will luve thee still, my dear.
To conclude, here’s a version of Burns’ poem using modern Scots spellings (of course there’s more than one way to spell Scots, and many people will disagree with some of my choices):
Och ma lae’s like a reid, reid rose,
That’s newlie sprung in Juin:
Och ma lae’s like the melodie,
That’s sweetlie played in tuin.
As fair art thou, ma bonnie lass,
Sae deep in lae am I;
And A will lae thee still, ma dear,
Till aw the seas gang dry.
Till aw the seas gang dry, ma dear,
An the rokes melt wi the sin;
An A will lae thee still, ma dear,
While the saunds o life sall rin.
An fare-thee-weel, ma ainlie lae!
An fare-thee-weel, a while!
An A will come again, ma lae,
Tho ’t were ten thousen mile!