The first verse of "Lincoln Boys" is reprinted in Cecil D Eby, Comrades and Commisars: The Lincoln Battalion in the Spanish Civil War, on page 111. No title is given. The verse is given as,

Oh, the Lincoln boys fought at Jarama
They made the Fascisti cry "Mama."
They held down the line
For months at a time
And for sport they would play with a bomb-a.

There's an asterisk on "bomb-a", which suggests there's a footnote somewhere in the book, but I don't have the book, I'm just looking at the one page on Google books.

The book may have some other songs of interest. On page 112 there are four verses of a Red River Valley parody starting "There's a valley in Spain called Jarama".