The Indiana University Sheet Music Collection has the sheet music, from which I transcribed this:

WHOSE IZZY IS HE (IS HE YOURS OR IS HE MINE)
Lew Brown, Bud Green, and Murray Sturm. 1924

VERSE 1: I know a guy named Izzy
And he's always busy
Making love to women ev'ry night.
One of them is Sarah.
What a holy terror!
She wouldn't give him up without a fight.
When she saw him flirting with a girl who lives next door,
She got so excited that she started in to roar:

CHORUS 1: Whose Izzy is he? Is he yours or is he mine?
I'm gettin' dizzy, watching Izzy all the time.
He said that he'd be true to me.
I should've got a guarantee!
Whose Izzy is he? Is he yours or is he mine?

PATTER: If you get him, then you'll give me the "Ha, ha, ha, ha, ha!"
If I get him, then I'll give you the "Ho, ho, ho, ho, ho!"
He who laughs last, laughs the best.
You laugh half. I'll laugh the rest.
You may laugh up your sleeve,
But I'll laugh up my vest. Hey!

VERSE 2: He went around with Jenny.
She was one of many.
He had lots of girlies on the side:
Becky Rose and Essie,
Sadie Belle and Tessie,
And each one thought she'd be his blushing bride.
Ev'ry time they saw him, they would form a great big ring,
They'd look at each other, and they'd all begin to sing:

CHORUS 2: Whose Izzy is he? Is he yours or is he mine?
I'm gettin' dizzy watching Izzy all the time.
He likes lemon with his tea.
I guess the lemon must be me.
Whose Izzy is he? Is he yours or is he mine?

CHORUS 3: Whose Izzy is he? Is he yours or is he mine?
I'm gettin' dizzy watching Izzy all the time.
I know he kissed you yesterday
'Cause I smelt garlic right away.
Whose Izzy is he? Is he yours or is he mine?

CATCH LINES: Making love is just his line,
But he is working overtime.

He said he'd marry me in spring,
But he is giving you the ring.

Just like a poor fish, I must wait
While someone else takes all the bait.

[The "catch lines" are printed after the end of the music. No explanation is given, but I assume they are meant to be used as lines 3 and 4 of additional choruses.]