Milk can have the lactose removed. It's still milk. Altered, but still milk. And it would still be an ingredient.

Of course, the original commenter does pull a bit of bullshit out of their ass. The term 'dairy-free' doesn't actually have any meaning. You can sell whatever you want and slap it on there without repercussion.

Which is irrelevant. See, the great thing about discussions is that they're incredibly dynamic. We don't have any obligation to remain on the exact same topic for the rest of our lives. We make tangents and comment on those tangents and eventually end up on a different topic. Sometimes it's still very similar, and other times you jump around from debating which pair of tits looks best to whether or not loreal makes good smelling shampoo.

So we have the original commenter who's pulling bullshit out of their ass (although does explain why lactose-free creamer could still have milk in it).

And then we have another commenter that's wondering why we would label it as dairy-free instead of lactose-free. At this point, the discussion has made a slight detour. We're now talking about why we would label it as dairy free instead of lactose free, when it would actually be lactose free.

And finally, we have the person who's been downvoted to oblivion saying that we call it dairy-free and not lactose-free because it has milk in it.

So at this point in time, the conversation has shifted from 'This is why that dairy-free creamer has milk in it' to 'Dairy-free creamer isn't called lactose-free creamer because it has milk in it.'

So, in accordance to what's currently being discussed, I said that's wrong, because it wouldn't have lactose in it. It would be lactose-free creamer.

We're not talking about the creamer in OP's image anymore. We haven't been for about five comments deep now. Try and keep up, will ya?