Hydrogenated Vegetable Oil or Fat is often contaminated with milk protein.
If you have a serious milk allergy, you should definitely avoid it.  If you
are simply lactose intolerant, I don't think it's necessary to eliminate it
from your diet.  See how it affects you.  Non-hydrogenated Vegetable Oil or
Fat is 100% dairy free.  For some reason milk protein is introduced through
the process of hydrogenating (or thickening) the oil/fat.  If the label does
not indicate hydrogenated or non-hydrogenated, call the company and ask
which is used or simply avoid the product.

Good luck.

Cheryl