Before bathing him, Lucy asks Louie if he wants a Henna Rinse. Henna Rinse was the hair dye that Lucille Ball (and her TV incarnations) used to make her hair that unique shade of red. It was comically portrayed on "I Love Lucy" as the first thing Lucy Ricardo would grab in case of a fire.
Six dogs appear here: Bob Williams' Louis, Mrs. Gordon's basset hound Winston, a bulldog named Teddy, a Yorkie named Tiger, a St. Bernard named Tinkerbell, and an unnamed dachshund.