I don't think the following information has been put into Mudcat before.
In the thread on The Barnyards of Delgaty the tune Linton Lowrie is named.
In a 1908 volume called Song Gems (Scots) The Dunedin Collection, are "a goodly number of forgotten and little known gems of song".
One is
Linton Lowrie
Words by James Ballantine, Music by Alexander MacKenzie [i.e. he is the composer, the tune is the one well known for the Barnyards]

I tint my hert ae morn in May
When birdies sang on ilka tree
When dewdraps hung on ilka spray
And lammies ply'd on ilka lea
Linton Lowrie, Linton Lowrie
Aye sae fond ye trowed tae be
I never wist sae bricht a morn
Sae dark a nicht wad bring to me

O Linton's words sae saftly fell
Sae pure the glamour o his ee
That I hae never been mysel
Sin ere he spak an keek't tae me
Linton Lowrie, Linton Lowrie
Come dear Lowrie back to me
An siccan love I'se bear to you
E'en your forgettin will forgie

His absence I'll nae langer bear
My grief I can nae langer dree
I'll gang a thoosan mile an mair
My Linton's comely face to see
O Linton Lowrie, Linton Lowrie
Gin you'll come to Loganlea
I'll mak ye laird o Logan Ha
And I your loving wife will be

The song is also in Sam Henry's Songs of the People.
There is a Loganlea in the south of West Lothian, and various candidates for Linton.