Billy tries to conceal the fact that Marmaduke has eaten an entire floor lamp, except for the shade.
Marmaduke is utilizing the cartoon rule which says that only a head cover is necessary to form the perfect disguise. In the Looney Tunes, a rabbit put on a wig and human men fell in love with him. In Hannah Barbera Cartoons, an animal would don a policeman's hat and everyone would afford him all the respect due a law enforcement officer. Therefore it only stands to reason that if Marmaduke wore a lamp shade on his head, everyone would think he's a lamp. Unfortunately Dottie has been overstressed and refuses to play along.
The question here is, what happened to the lamp?