Hi,
I believe I read somewhere that lactose free milk does actually have lactose in it, but they have added lactase to digest? the lactose, so you will still have the lactose sugar content..... Found this:

Milk is made lactose free by adding the lactase enzyme to regular milk. Lactase breaks down lactose into the two simple sugars--galactose and glucose--which combine to form it. The resulting milk is usually sweeter than regular milk due to the fact that these two sugars are sweeter separately than they are when combined into lactose.