In my opinion, the best lactose free milk has some lactose filtration in the process. The brands that just dump lactase on the milk without filtering lactose are actually sweet, like they dumped a bunch of sugar in it.
But, if one is about to make a milk powder, then it is possible to remove the split lactose sugar crystals. But it's not milk anymore..
From my understanding they take advantage of lactose being smaller than milk and they just get the milk "stuck" in the filter and then throw out the unfiltered lactose.
This is mostly used as a preprocessing step for cheese production, but by rehydrating you get ultra-filtered milk, which are lactose-free and not sweet.
So it's possible. Thank for pointing out.
The enzymes take 1 sugar (lactose) and break it down into 2 sugars (glucose and galactose).