Songs mentioning lassies milking include:--

"The {Old] Yellow Haired Laddie"    [at least two others with this name]
Mentioned by Allan Ramsay B.1686 as an old song in his day.

[1] The yellowed haired laddie sat doon on yon brae
    Cried milk the yowes lassie let nane o them gae
    And aye as she milket she merrily sang
    The yellow haired laddie shall be my gudeman.

On another recent thread I mentioned that I had a number of floating songs which, as far as I can determine, do not appear in any of the printed collections--one of them being:--

"Lassie Leave yer Milkin Pail"

[M] [1] O lassie lea yer milkin pail
         O lassie lea yer fee
         O lassie lea yer milkin pail
         An come awa wi me.

[F] [2]
[M] [3]----I have recently found this one verse in an 1820s.
            publication.
[F] [4]
[M] [5]
[F] {6]