Lady is one of the titular characters in Disney’s 1955 animation and 2019 live-action Lady and the Tramp films.
Lady is an American Cocker Spaniel. She is voiced by Barbara Luddy in the animated film.
In the live-action Lady and the Tramp film, Lady is played by a dog called Rose. According to the New York Post, Rose is an American Cocker Spaniel and hunting dog from Texas.
Source: https://nypost.com/2019/11/06/meet-the-real-dogs-of-disneys-new-lady-and-the-tramp/