I think this is the Lomax MS text you quote, Stewie. The book is "Songs of the Cowboys," N. Howard 'Jack Thorp, Variants, Commentary, Notes and Lexicon by Austin E. and Alta S. Fife, 1966.

XIII-F. "The Cowboy's Lament"
Lomax d.5656, from Slim Critchlow (JL. 320).
On p. 165-166, 10 verses, no date.
As I was walking by Tom Sherwin's bar room
Tom Sherwin's bar room so early one day- etc.
(No "battle" here- Please gather up my last hand of poker
The one that I dropped when I got my death wound, etc. No stanza with that word in the Fifes' long summary, pp. 148-190.)

Two more MS excerpts from Lomax are the music for two versions of "Tom Sherman's Barroom." No dates.
XIII-T "Streets of Laredo" LC 658B2, sung by L. Henson, Texas, recorded by Lomax (FAC I 292). "As I was riding down past Tom Sheridan's bar-room, One morning so early in May, I spied," etc. p. 180-181.

XIII-U. "Streets of Laredo" LC 936B2, Texas, 1937, recorded by Lomax (FAC I 293). "As I passed by Ben Sherman's bar-room, Ben Sherman's bar-room quite early one morn, I spied " etc. p. 181.

In Cowboy Songs, 1910, Lomax printed the "Cowboy's Lament" beginning "As I walked out in Laredo one day," etc., 15 verses. No comments or date.
In "Cowboy Songs and Frontier Ballads," 1938, p. 417-422, the Lomax's printed 12 verses of "As I walked out in Laredo" with 2 more in italics, with several variant verses in footnotes. Listed as the beginning stanza in one version (no attribution) is:
As I passed by Tom Sherman's barroom
Tom Sherman's barroom quite early one morn,
I spied a young cowboy all dressed in his buckskins, All dressed in his buckskins and fit for the grave.

He gives the first verse of another (no attribution)
As I rode up to the fragrant barroom
As I rode up to the barroom one day.

In "Folksongs of North America, 1960, Alan Lomax dropped the previous versions and used another text- "from p. 417 of "Cowboy Songs,"- but it is not!. He gives a version of Tom Sherman's Barroom instead. No attribution.
As I rode out by Tom Sherman's barroom,
As I rode out so early one day,
'Twas there I espied a handsome young cowboy,
All dressed in white linen, all clothed for the grave.
(Alan Lomax, getting quite upscale in his language).

Stewie, does this help? Looks like the Fifes, in the volume you have, used still another version. I don't have their "Cowboy and Western songs." In the volume I have, they say that they have 150 texts- Laredo 39, Tom Sherman 37, Laden, Laterin, etc. 25, Various, inc St. James, Austin's fair city, etc. 31, and without localization, 18 (odd, in this list they don't mention Galveston which is included in their reprint of Thorp's booklet of 1908.)