Here is a simplified explanation for choosing formulas with suspected
allergies/ intolerances. Formulas have two main ingredients(besides water)-
sugar and protien. Lactose is the main sugar in breastmilk and cows milk,
sucrose and corn syrup are in soy milk and the hypo-allergenic formulas.  Cow
protiens are in cows milk, soy protiens in soy milk, and chemically or heat
altered or broken down protiens are in the Nu--------n et al.
Allergies are a response to foreign protiens.
Lactose problems are usually due to enzyme (lactase) deficiencies. The gut
cannot completely break down the lactose or other disaccharides (two part
sugars). Resulting in gas, diarrhea, pain, or bloating. Most problems are a
relative problem, not a complete lack of the needed enzymes. The enzyme needed
for lactose is highest in infants and declines with age. Depending on the
ethnic group 20-80% of adults cannot digest lactose well.
I still cannot figure out what lactose-free cows milk formula is for.
Congenital lactase deficiency is very very very rare. In spite of what we were
once taught acquired lactase deficiency in infancy does not occur in most
cases of simple or moderate diarrhea.
If a baby does well on breast milk, but not cows milk formula the problem
cannot be lactose. Dairy in mom's diet would not change the lactose content,
but might alter the protiens.
When I switch formulas in suspected allergic infants, I use a non-cow/ non-soy
ABM because there seems to be a bit of overlap between cow and soy protiens. I
always tell the parents to give the baby at least a week after the change.
Sometimes I think I am just buying time until the baby's gut matures a bit,
the parents calm down, or the baby outgrows her colic. I do have a few truly
allergic infants who develop hives and swelling with the ingestion of cow milk
protiens, otherwise I suggest they go back to a less expensive formula after
3-4 weeks. Most infants tolerate cows milk by age one even if they had a lot
of symptoms on cows milk as infants.

Mary Murphy MD