When a cat will not eat and is lethargic, it can signify a serious problem, according to WebMD, and can be caused by illness, as a side effect of a recent vaccination, traveling to unfamiliar surroundings or even due to a psychological problem or being finicky. A cat must use stored fat for fuel when it doesn't eat, and this fat must be processed by the cat's liver, which is a step that requires adequate protein; cats that are not eating soon exhaust supplies of protein, and their livers can be overwhelmed by the process of using the fat, which makes not eating very dangerous for cats.
A number of illnesses in cats can cause them to alter their eating habits, including pancreatitis, cancer, intestinal problems, kidney failure and infection. The problem need not be serious, however, for a cat to stop eating as it normally would. A simple toothache can even cause the cat to stop eating. If a cat has a recent vaccination, loss of appetite can sometimes occur and should be mild and temporary.
Because the loss of appetite in a cat can be a serious problem, it is important to have the cat evaluated by a veterinary professional as soon as realizing the cat's eating habits have changed.