I have a different version of Logan Water attributed to John Mayne, circa 1781 which would make him a contemporary of Burns.

LOGAN WATER

By Logan's streams that rin sae deep
Fu' aft wi' glee I've herded sheep
Herded sheep or gathered slaes
Wi' my dear lad on Logan braes.
But wae's my heart, thae days are gane
And fu' o' grief I herd my lane
While my dear lad maun face his faes
Far, far frae me and Logan braes.

Nae mare at Logan kirk, will he
Atween the preachin's, meet wi' me
Meet wi' me, or when it's mirk
Convoy me hame frae Logan kirk.
I weel may sing, thae days are gane
Frae kirk and fair I come alane;
While my dear lad maun face his faes
Far, far frae me and Logan braes.

At e'en, when hope amaist is gane
I daunder out or sit alane,
Sit alane beneath the tree
Where aft he kept his tryst wi' me.
O! could I see thae days again,
My lover skaithless, and my ain
Beloved by friends, and far frae faes
We'd live in bliss on Logan braes.