Eleanor, please check out the feature song at Prof's Irish Pages....it is Danny Boy.....and tells about Weatherly (the author of these lyrics).... here's the link:
Prof's Pages http://www.prof.co.uk/irish1.htm
But to specifically answer your question I quote the following from Prof's Pages (some of the research to which I contributed):
"The "song" Danny Boy was written by one Frederic E. Weatherly.. that is the lyrics. Actually, in 1910 he had written the lyrics to go with music he composed himself, but the song failed. Interestingly, his sister-in-law sent him the melody (commonly refered to as The Londonderry Air) from America and noticing it fitted the lyrics he had written, he published it in 1913."
As for the tune, Robinson's site on Danny Boy (link in Prof's feature song page) and Bruce Olson's site (link on the Robinson page) show a tune entitled Aislean an Oigfear, translated: "Young Man's Dream" from the Bunting collection of 1796 that seems to be the origins for the "modern day melody" (which was first published by George Petrie in 1855 as "Unknown" and came to be called "Irish Tune From County Derry"...).
I haven't come across mention of the tune title "The Lass so Good and True".....will need to try to seek it out.
There's lots of interesting info about the song at the Prof's and Robinson's sites....well worth checking out!
Cheers,
Mary