I have been diagnosed as LI but my symptoms also go way beyond the symptoms
usually attributed to LI. I don't get headaches or vomit but I do suffer
from the latter two that you mention.  The diarrhea comes within 6 hours
and the lethargy and feeling unwell come in 36 hours or so.

The reason why Lactaid pills don't work is that they deal with the LI
symptoms exclusively. I think you should  consider that your daughter has a
dairy allergy and react accordingly. There might be other reasons, but if
total elimination of dairy works, then go for it. That is what I did and it
has worked for me. By the way, some LI symptoms are quite close to
Irritable Bowel Syndrome and Doctors may diagnose a problem as that.

Don

 My question;  My
>daughter's symptoms do not seem to be at all typical for LI, although the
>onset does appear to be initiated by ingestion of milk products.  Her
>symptoms include headache, vomiting, lethargy and diarrhea. She becomes
>very pale, and her headaches are similar to migranes (i.e. sensitive to
>light, etc)