I'll get to books using this title perhaps a bit later.

The NYPL's Lincoln Center Dance Collection had one clipping about a

dance with this "Gay Life" title. It's from the Hearst Sunday Magazine (NY

American, LA Examiner, and other newspapers), copyright 1911. A November

1911 date is in an article on the other side of the clipping.

"Gay Life" is "An erring woman's dance, portraying her career from the

dawn of girlish, innocent beauty, through the old, familiar stages to

inevitable despair and death. This is the dance by Louis La Gai, which is

said to have 'made Paris Good.' (...) It is said that the dance by Louise La

Gai (Louis or Louise?--ed.), at the Theatre Marigny, sent gay Parisian

audiences away with tears in their eyes, because of the terrible vividness

with which it depicted the temptations which may assail any woman, and

because it showed that for the woman to yield meant no end but that of a

despairing death. The effect was, perhaps, all the keener because the dance

was programmed 'The Gay Life.'"

For whatever this is worth, it's a "Gay Life" dance and a choreographer

named "Gai" in "Gay Paree."

Incidentally, OED has "Gay Paree" for 1930.