Lactase is the enzyme which is required to digest lactose. The symptoms of lactose intolerance are liquid, frothy stools, and an irritable baby who may pass wind often. If a baby is lactose intolerant, the medical tests, 'hydrogen breath test' and tests for 'reducing sugars' in the stools would be expected to be positive. However these are positive in most normal babies under three months too so their use in diagnosing lactose intolerance is open to question. If a mother is lactose intolerant then her baby will be as well.
Lactose intolerance is the same as intolerance or allergy to cow's milk protein.
Anything that damages the gut lining, even subtly, can cause secondary lactose intolerance. This confusion probably arises because cow's milk protein and lactose are both in the same food, ie dairy products. Also contributing to this confusion is the fact that allergy or intolerance to this protein can be a cause of secondary lactose intolerance, so they may be present together. Secondary lactose intolerance is a temporary state as long as the gut damage can heal. When the cause of the damage to the gut is removed, for example the food to which a baby is allergic is taken out of the diet, the gut will heal even if the baby is still fed breastmilk.