Murray on Saltspring says in his previous post that J.W. Holder was the composer and William Holder wrote the words.
I was able to find this reference to the composer on line (didn't copy the entry in its entirety):

British Musical Biography: A dictionary of musical artists,etc by James Duff Brown, Stephen Samuel Stratton 1897

Holder, Joseph William organist and composer born in Clerkenwell, London 1764. A chorister in the Chapel Royal, etc etc . Died in 1832
Collection of catches, canons and glees, op. 6 1787 collection of songs, duets and glees 1800 … Lassie would ye love me Scots song.

I haven't been able to find out more about him, all the references I have found list the words as Anon or Trad.

There was a Rev. William Holder listed in the same Biography but he predated JW (born in 1616).

Anyone able to fill out this information? I don't have access to Whitelaw, Book of Scottish Song (1844), but it sounds to me like Murray's source was someone else anyway.