Denise,
Milk sensitivity is an allergic response due to a protein, possibly cow
immunoglobulins or casein proteins.  sugars are generally too small and too
simple in structure to provoke allergic reactions.  If an infant is truly
allergic to bovine (cow) proteins in maternal milk, the mother needs to stop
eating/drinking dairy products.  She might do better with sheep or goats milk
products, as the proteins are different.  Note that most mothers do not pass
whole dietary proteins into their milk, there seems to be some sort of
processing/digestion deficit in moms that have a family history of allergy.
        Lactose intolerance is an inabilty to break lactose into it's component
sugars, glucose and galactose, due to deficiency of lactase (the enzyme that
splits lactose).  This is rare in infancy, but common in some ehtnic groups
after infancy.  Long term breastfeeding (past age 2 years) has been shown to
prevent later lactose intolerance.  If the baby is truly lactose intolerant,
lactaid dripped onto the mother's nipples immediately before latching on can do
the trick.
        Beware of confusing a relative lactose overload from breastfeeding
mismangement with lactose intolerance.  This occurs when a baby gets mostly
foremilk from infrequent breastfeedings (which lower prolactin levels, which
decreases both milk supply and fat content) or timed breastfeedings (switching
breasts before the infant gets the high fat 'hindmilk'.)  Infants who are
allowed to bf on cue for as long as they desire seldom have this difficulty.
The symptoms are screaming from abdominal pain with greenish, usually frothy
stools.
Catherine Watson Genna, IBCLC