This is the important traditional version with her full name from Ireland as reported in Ulster Folklife - Volume 18 - Page 36 by Hugh Shields in 1972. I give it here as best figured out without a copy of the book. Anyone that has details please provide them.
"Molley Bann Lavery" pre1845 from County Down, Ireland from oral tradition; Hugh Shields 1972
[1st] It's all you young men that carry a gun, Beware of late fowling at the setting of the sun, Concerning a young man that happened of late, That shot Molley Bann Lavery — her beauty was great.
[2nd] He being late fowling he shot her in the dark, But oh and alas, he did not miss his mark! With her apron about her he took her for a cran, But oh and alas, it was poor Molly Bann!
[3rd] But when he went to her and found she was dead Abundance of tears from his eyes he has shed; He went home to his father with his gun in his hand Saying, — Father, dear father, I have shot poor Molley Bann.
[4th] It's out bespoke his father, his hairs they were gray, My son, take my blessing and don't run away. Stay in your own country your trial to stand And you will not be condemned by the laws of the land.
[5th] O father, dear father, I must go away For in this country I never could stay; I shot Molley Bann Lavery and she was my darling, The pride of the North and the Flower of Kilwarlin.
[6th] The maids of this country they are all very glad Since Molley Bann Lavery the beauty is dead, But gather them together and put them all in a row: She appears in the middle like a mountain of snow.
[7th] She appeared to her uncle as it were in a dream Saying, — Uncle, dear uncle, James Reynolds don't blame; With my apron being about me he took me for a cran, But oh and alas, it was I, Molley Bann!
[8th] In Lisburn she was born and in Lurgan educated But oh, in Kilwarlin poor Molley was defeated! With her apron being about her she was taken for a cran, But oh and alas, it was poor Molley Bann!