human biology - Lactose Intolerance

The lactose intolerance Wikipedia page explains the problem fairly well, so I'll refer you to that for a more detailed explanation.

Briefly, the most common cause of lactose intolerance is primary lactase deficiency, which affects the majority of the world's population. This only affects adults: the majority of people do not produce lactase as adults.

Congenital lactase deficiency, instead is a very rare, autosomal recessive genetic disorder that prevents lactase expression from birth.
[...]
Congenital lactase deficiency (CLD), where the production of lactase is inhibited from birth, can be dangerous in any society because of infants' nutritional reliance on human breast milk during their first months. Before the 20th century, babies born with CLD often did not survive, but death rates decreased with soybean-derived infant formulas and manufactured lactose-free dairy products. Beyond infancy, individuals affected by CLD usually have the same nutritional concerns as any lactose-intolerant adult.

A couple of good references:

Lactose intolerance in infants, children, and adolescents. - Heyman, Pediatrics 2006

Genetics of lactase persistence and lactose intolerance. - Swallow, Annu Rev Genet. 2003