I found these lyrics at Rabid Squirrel's Jazz Archive, and I can't vouch for the quality of the transcription. The song was recorded in 1953 by Jaye P. Morgan (hey - I thought gigolos were male). Also recorded by Bing Crosby, and I think Louis Prima also did a recording of this song.
In 1985, David Lee Roth recorded "Gigolo" in medley with the 1916 song, "I Ain't Got Nobody."


JUST A GIGOLO
(Irving Caesar and Leonello Casucchi)

I'm just a gigolo
Everywhere I go
People know the part I'm playing

Paid for every dance
Selling each romance
Every night some heart betraying

There will come a day
Youth will pass away
What will they say about me?

When the end comes, I know
They'll say just a(nother) gigolo
Life goes on without me