Loss of appetite, lethargy, and excessive lying down in a cat can be caused by a variety of reasons. Here are some possible causes and corresponding solutions:
1. Dietary issues: Check if the cat's food is expired or unsuitable for its appetite. Try switching to a fresh food, or consult a veterinarian for a special diet recommendation.
2. Illness or Infection: If your cat exhibits other symptoms such as vomiting, diarrhea, or abnormal body temperature, it may be suffering from an illness or infection. Take your cat to a veterinarian immediately for a full examination. 
3. Environmental issues: The cat may be stressed or not adapting well to changes in its environment. Provide a quiet, warm, and comfortable environment, and try to keep it stable.
4. Lack of exercise: Cats may lack sufficient exercise, leading to lethargy. Provide adequate playtime to keep your cat active.
5. Psychological problems: Some cats may experience psychological problems such as anxiety or depression. Observe changes in your cat's behavior and seek help from a veterinarian or behavior specialist as soon as possible.
