No, it is not recommended to feed cats limes or any other citrus fruits. Citrus fruits like limes, lemons, oranges, and grapefruits are highly acidic and can cause digestive upset, including vomiting and diarrhea, in cats. Additionally, the oils and compounds found in citrus fruits can be toxic to cats, which can lead to various health problems. Therefore, it's best to avoid feeding limes or any other citrus fruits to cats and stick to a balanced and nutritionally complete cat food recommended by a veterinarian. If you suspect that your cat has consumed lime or any other citrus fruit, it's best to consult with a veterinarian immediately.