> Can anyone tell me definitively if lactose has dairy protein?

Pure lactose would by definition have no protein, because it
is a sugar -- not a protein.  In the real world, however,
nothing is ever pure.  As long as a substance comes from a
dairy source the only question is whether the amount of
impurity in the form of proteins is more than you personally
can deal with.  Only you can answer that.  It is clear from
anecdotes related here over the years that even medicinal
grade lactose contains enough residual protein to be a
problem for people with severe, anaphylactic level
allergies.

This same principle applies for other milk
ingredient issues, like casein versus whey proteins.  Some milk-related  substances, such as lactic acid, can come
from non-dairy sources.  For those, if you confirm a
non-dairy source, the contaminants would not likely include
milk proteins.  I don't believe there are any non-dairy
sources for lactose.

Bob