The 1933 book The Life Story Of Eamon De Valera by Sean O Foalain (p. 10) seems to have a very similar sinppet, though it's slightly different:

Up De Valera, you're the champion of the right,
We'll follow you to battle 'neath the orange, green and white,
And when next we meet the Sassenach, we'll beat him.
Oh, we'll beat him in the fight--
And make De Valera King of Ireland!

Identical text can be found in The Courier-News of Plainfield, NJ on May 18th, 1937 p. 7

A similar excerpt from Comparative Criticism: Volume 19, Literary Devolution: Writing in Scotland, Ireland, Wales and England by E. S. Shaffer quotes from the play "At the Black Pig's Dyke" by Vincent Woods, which has the following similar (but again slightly different) lines. Note that, given the setting, it's very possible they're not "authentic" lines.

Up de Valera, you're the champion of the fight,
We'll follow you to battle 'neath the orange, green and white,
And when next we meet the Sassenach, we'll beat him.
Oh, we'll tackle Eoin O'Duffy and we'll roll him in the shite
And we'll crown de Valera King of Ireland!

An additional version can be found in Iris Murdoch: A Life by Peter Conradi:

Here's to De Valera,
The hero of the right,
We'll follow him to battle,
With orange green and white.
We'll fight against old England
And we'll give her hell's delight.
And we'll make De Valera King of Ireland.

Versions highly similar to a combination of a several of these but with nothing new to offer can be found in Eamon de Valera by M. J. Macmanus and IRA Jailbreaks 1918-1921 by Florence O'Donoghue.

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Though the Battle Hymn does work as a base for the lyrical theme,
when I first read it I thought it scanned well to Yellow Rose of Texas. It's a much more peppy tune which seems to fit with the energy the song was often described with.