The "Max" the people in the commentary refer to after Lucille sang is almost certainly renowned Missouri and Arkansas folklorist Max Hunter, whose collections are held at Missouri State - click. Sadly, it doesn't seem as if Ms. Lucille reported the song to Max.

It does bear some resemblance to a song in that collection, How Come That Blood On Your Coat Sleeve, specifically the 6th stanza. This song is related to Edward as posted by Joe above (read more). I'll copy the whole song below.

How Come That Blood On Your Coat Sleeve
Cat. #0253 (MFH #175) - As sung by Mr. Clyde Johnson, Fayetteville, Arkansas on October 1, 1958

VERSE 1
How come that blood on your coat sleeve
My son, come tell it to me
It is th blood of th little yellow pony
That plowed a fur for me, me, me
That plowed a fur for me

VERSE 2
O, it tis too red for that
My son, come tell it to me
O, it is th blood of th little guienie gay halk
That sailed away from me, me, me
Sailed away from me

VERSE 3
O, it tis too red for that
My son, come tell it to me
O, it tis th blood of the little yellow pony
That plowed a fur for me, me, me
That plowed a fur for me

VERSE 4
O, it tis too red for that
My son, come tell it to me
O, it tis th blood of my dear ole brother
That rode aside of me, me, me
Rode aside of me

VERSE 5
What you an' your brother fall out about
My son, come tell it to me
We fell out about that sycamore bush
That might a made a tree, tree, tree,
That might a made a tree

VERSE 6
O, what'a you gonna do when your Father comes back
My son, come tell it to me
I'll set my foot on yonder ship
An' sail across th sea, sea, sea
An' sail across th sea

VERSE 7
O, what'a you gonna do with your pretty little children
My son, come tell it to me
I'll leave them here for my dear ole Mother
To keep her company, nee, nee
To keep her company

VERSE 8
O, what'a you gonna do with your house and barn
My son, come tell it to me
I'll leave them here for my dear ole Mother
To raise my chilren on, non, non
Raise my children on

VERSE 9
O, what'a you gonna do with your pretty little wife
My son, come tell it to me
I'll set her foot on yonder ship
An' sail across th sea, sea, sea,
An' sail across th sea

VERSE 10
O, when you gonna come back
My son, come tell it to me
O, I'm not coming back till th sun and th moon
Both set in the North, and I'm sure it'll never be, be, be
An' I sure it'll never be