The Archive of Popular American Music at UCLA also has a copy of the sheet music, minus its cover. I have put the words in boldface that were missing or wrong in the transcription above. I also put 4 lines of each chorus in italics so you can more easily see how the 2 choruses differ.

THE IRISH WERE EGYPTIANS LONG AGO
Words, Alfred Bryan. Music, Chris Smith.
From "Shubert Gaieties of 1919"
New York: Jerome H. Remick & Co., © 1920.

VERSE: I've studied things Egyptic,
Those writings weird and cryptic
Upon the tombs that dot Sahara's sands.
I've solved each strange inscription
Left by each wise Egyptian
And hold the mystic secret in my hands.
The Irish were Egyptians long ago.
Just read between the lines and you will know.

CHORUS 1: It must have been the Irish who built the pyramids,
For no one else could carry up the bricks.
It must have been a Doyle who dug the river Nile,
For no one but an Irishman would fight a crocodile.
  I think these Micks were Turks, Mohammedans and Ghurks.
  They speak of "Irish Turkey" till today.
  Cleopatra was a colleen who came from Connemara.
  She lost her nationality while roaming in Sahara,
So all the Hooligans and all the Dooligans
Must have been Egyptians long ago.

CHORUS 2: It must have been the Irish who built the pyramids,
For no one else could carry up the bricks.
It must have been a Doyle who dug the river Nile,
For no one but an Irishman would fight a crocodile.
  Now ev'ry Houlihan once drove a caravan.
  I'll say the same for ev'ry Mac and O,
  And when Moses went to Egypt and saw those Irish faces,
  He took the name O'Callahan and chang'd it to Oasis,
So all the Hooligans and all the Dooligans
Must have been Egyptians long ago.