The lyrics are about a woman who has her own priorities in life and who is not interested to play with New York high society stereotypes. Hence she is dismissed as a Tramp. The original lyrics are more explicit than subsequent versions and portray dated references to mid '30s New York urban life and culture.
Fiorello La Guardia was elected mayor of New York Mayor in 1933 and obviously his electoral base was not the Manhattan elite but the middle-class (Italian and German immigrants, Jews, some Democrats and Socialists ...)
George VI and Queen Elizabeth's coronation was in 1937 and most of Manhattan elite (the people who played with Earls and Barons) was interested in the ceremony in London.
Mulligan stew, is a dish said to have been prepared by American hobos in camps in the early 1900s.
Ritz hotel is a New York luxury hotel on Central Park.
Sardi's is a New York restaurant that opened in 1927 in 234 West 44th Street (between Broadway and Eighth Avenue, where still is).
Noël Coward was a British actor and director, very popular in '30s. He is known for his sophisticated comedies and influence on American culture.
Beaux Arts Ball was held in 1931, in New York, when famous architects dressed up as their buildings.
Dinner at Eight quote is self-explanatory but also the title of a 1933 movie: a comedy of manners about the life of a high class New York magnate family, inviting at dinner some Peers from England (Lord and Lady Ferncliffe) as a sign of social distinction, but the dinner turned out in disaster.
Tony Bennett and Lady Gaga recorded a version of this song for his 2011 album Duets II. Bennett praised Gaga's performance in the song, saying that she is a real "jazz lady". They performed the song live on ABC's Thanksgiving special dedicated to, written, directed, produced and hosted by Gaga entitled A Very Gaga Thanksgiving. They were the opening number, singing next to an old piano in a casual obscure room. Gaga played the part of a "tramp" with class and style Bennett said, "I see in Lady Gaga a touch of theatrical genius, she is very creative and very productive, I think as time goes on she might be America's Picasso. I think she's going to become as big as Elvis Presley."  The song, even though not officially released got to enter the Japan Hot 100, where it has managed to enter the top 40 and it has also entered the top 200 extension to the UK Singles Chart.
Following the single, Bennett drew a sketch of Gaga naked for the January 2012 issue of Vanity Fair, which was then auctioned for $30,000. The money raised went to charity, supporting the Exploring the Arts (ETA) and Born This Way Foundation.
The song as well as the video received critical acclaim for the vocals of both Bennett and Gaga as well as for the simplicity of the video, which departs from Gaga's usual efforts. The song received praise from both E! and MTV. Other critics expressed hopes that Gaga would release her own jazz music after this successful effort.
The song was also added to Cheek to Cheek: HSN Deluxe album bonus tracks duet between Lady Gaga and Tony Bennett released in September 2014.
The duo filmed a music video for the track. The video shows Bennett and Gaga singing "The Lady Is a Tramp" together in a studio in front of music stands. The video, like the song's lyrical content, received largely positive critical reception.