According to Wikipedia most mammals stop producing or decrease production of lactase after weaning.
Lactase is essential to the complete digestion of whole milk. Lactase breaks down lactose, a simple sugar which gives milk its sweetness. Lacking lactase, a person consuming dairy products may experience the symptoms of flatulence, diarrhea & nausea
In general, how concerned do I need to be? If my pet is lactose intolerant, does that mean they can't have any dairy products?