I think your ped is probably confusing lactose intolerance with something
else.  Lactose intolerance (lack or low level of lactase) in infants is quite
rare but can be either congenital, in which case the baby would be
symptomatic after very first feed, or secondarily caused by damage to
intestinal mucosa following severe diarrhea.  Unfortunately, I can't find the
reference on incidence of LI in infants, but it's rare.  In older children
and adults lactose intolerance results from a gradual decline in lactase
production, usually after age two.

You might investigate a more likely cause of the baby's symptoms, allergy to
something mom is eating.  Often cow's milk, egg, nuts and other common
allergens eaten by mom cause symptoms in breastfed babies.  Mom should keep a
three day or so log of what she eats, when baby eats, and baby's symptoms.
  Also, is the baby eating anything other than milk?

Sanna James, M.S., R.D.
Editor, Tiny Tummies
Mill Valley CA