Better give up, Robin. You would die of thirst if you looked for Tom Sherman's Barroom in Laredo. It was in Dodge City, Kansas.
Date 1876 when Maynard wrote the song- see Dr. James F. Hoy, "F. H. Maynard, Author of the Cowboy's Lament," Mid-America Folklore, vol. 21#2, Fall, 1993, pp. 61-68. Maynard based the song on "The Dying Girl's Lament," which is the form in which the British Isles song was picked up by the cowboys.
The song got moved to Laredo- and other places- later.

Fort Dodge was built in 1865 and the town got started about the same time. Some 1200 people in 1876. The cattle drives ended 1885-1890.