>Lactaid 100 milk is labelled as "100% lactose reduced"
and also as "lactose free" (both labels printed at
separate places on the milk carton).  Does anybody
know how to interpret this?<

Milk labeling falls under state laws rather than federal 
laws for some particulars. In this case, state laws allow 
"lactose-free" milk to contain up to one-half of 1% lactose. 
And Lactaid confirms that this is indeed true.  So consider 
the milk 99.5+% lactose-reduced.

This is still a very tiny amount.  My estimate is that there 
is the same amount of lactose in a cup of lactose-free 
Lactaid as there is in the film that sticks to a teaspoon after 
it is emptied of regular milk.

Of course, the milk protein remains so no one with 
milk allergy should consider it.

Steve Carper