There are no Siamese cats in the original 1955 Disney animated film Lady and the Tramp.
The cats in the film are mostly grey or black alley cats. The most prominent cat is "Si" (short for "Siamese"), a black cat with a white chest patch, but he is not a Siamese breed.
The confusion may arise because Siamese cats were popular in the 1950s and often appeared in cartoons, but they are not represented in the original film.