The cat shown in the Disney movie "Lady and the Tramp" is a Siamese cat. The cat's name is Si and he is portrayed as mischievous and scheming, causing trouble for Lady and the Tramp throughout the movie. The Siamese cat breed is known for its distinctive appearance, with a sleek body, pointed ears, and blue eyes, and it is also known for being vocal and intelligent. While Siamese cats can make great pets, they do have a reputation for being demanding and high-energy, and they require plenty of attention and stimulation to keep them happy.