Both broken English and Dutch lyrics to "Bye, bye, my Roseanne," here:
http://www.trossenlos.com/Shanties/Bye,%20bye,%20my%20Roseanna.htm
Bye, Bye, my Roseanna

Following the title is "(Bron: Jan Verbiest)"
A note in Dutch mentions verses by Johnny Collins and Jimmy Mageean and the cd "Coming of Age."

A further note calls it a 'parting' shanty, and says it was collected from Blacks in the vicinity of Beaufort, North Carolina.
No mention of Lomax, but this may be where he ties in.

Lyr. Add: BYE, BYE, MY ROSEANNE
(Bron: Jan Verbiest)

1.
Oh, Rosiann, my Rosiann
byebey, my Rosianna
Oh, Rosiann, sweet Rosiann
I will be home tomorrow.

Chorus:
ByeBye, ByeBye, ByeBye, ByeBye,
ByeBye my Rosianna
ByeBye, ByeBye, ByeBye, ByeBye,
And we all be home tomorrow.

2.
I ship-ped and sail-ed around the bank.
koor*; Byebye, my Rosianna
Oh load it down with Fisherman
Koor; I will be home tomorrow.
*koor = chorus response

Chorus

3.
Oh a dollar a day is a fisherman's pay
koor; ByeBye, my Rosianna
It's easy come, easy go away
koor; I will be home tomorrow

Chorus

4.
We'll bound away across the bay
koor; ByeBye, my Rosianna
We bound away at break of day
koor; I will be home tomorrow

Chorus

5.
So Rosiann, my Rosiann
koor; ByeBye, my Rosianna
Oh Rosiann, sweet Rosiann
koor: I will be home tomorrow.

Chorus

I have not changed any of the spelling or capitalization. Note that the last line of each verse begins 'I will,' not 'I won't'.

I seem to recall "We're bound away across the bay" belongs to a song that das discussed before on Mudcat (Goodbye, my lover, goodbye?). Anyone remember it and the thread number?