Answering some questions about the ellusive 'novel'
All info from: http://en.wikipedia.org/wiki/Lady_and_the_Tramp
I know there's been a lot of speculation as to the relevence the film has to the novel, so hopefully this will clear some things up (and maybe even give you fans some great fic ideas!)
Originally, the film idea was inspired by Disney story man, Joe Grant, when he told Disney of the antics of his Springer Spaniel, Lady, who was 'pushed aside' for Joe's new baby. Disney liked the idea, but even though Lady was cute, he didn't think her story was all that interesting.
In the early 1940s Walt read a short story written by Ward Greene, "Happy Dan, The Whistling Dog", in Cosmopolitan Magazine. He thought Grant's story would be improved if Lady fell in love with a cynical dog character like the one in Greene's story, and bought the rights to it. The cynical dog had various names during development, including Homer, Rags, and Bozo, before "Tramp" was chosen. It was first thought "Tramp" wouldn't be acceptable because of the sexual connotation associated with the word ("The Lady is a Tramp"), but as Walt Disney approved it was considered safe.
Aunt Sarah's "Nip and Tuck" were later renamed Si and Am.
Originally, Lady's owners were called Jim Brown and Elizabeth. These were changed to highlight Lady's point of view. They were briefly referred to as "Mister" and "Missis" before settling on the names "Jim Dear" and "Darling".
In 1949 Grant left the studio, but Disney story men were continually pulling Grant's original drawings and story off the shelf to retool. A solid story began taking shape in 1953, based on Grant's storyboards and Greene's short story.
Greene later wrote a novelization of the film that was released two years before the film itself, at Walt Disney's insistence, so that audiences would be familiar with the story.
I couldn't find any other information on Greene's novelization of the film, nor could I find where one could buy this alleged novel. As for "Happy Dan, The Whistling Dog", you might be able to dig up that story if you can find anyone with a vintage 1940's issue of Cosmopolitan Magazine, but that would be a very rare find.
Hopefully, this clears some things up. It may also make sense as to why no one can find the original novel of "Lady and the Tramp".