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As an addition to Bill Elkus's posting on lactose intolerance, I will
mention that about 80% of Northern Europeans are lactose tolerant as adults
(through maintenance of their levels of the enzyme lactase), but that leaves
20% who are lactose intolerant as adults.  Throughout much of the rest of
the world these numbers are reversed, with about 80% of the populations
intolerant of lactose as adults.  If you are someone with celiac disease who
happens to be among the 20% (or 80% in the second case) who are lactose
intolerant, you probably will not be able to tolerate lactose even when
largely recovered on a gluten-free diet because your lactase levels have
declined in what is a largely normal process after the need for digestion of
breast milk (with high lactose levels) has disappeared.  I have heard,
however, that lactose intolerant individuals can usually tolerate small
amounts of lactose, but, say, consumption of a large glass of milk would
probably get to them pretty quickly.

Don Kasarda