Original Parmesan cheese is lactose free after 12 months of seasoning (good ones are generally 24-48 months). The one in the picture says 2012, so it's safe to assume that your daughter can eat the whole wheel and not be affected by the lactose intolerance at all!
They use the ones that are culled for making milk. Bunch of male calves that the dairy industry has no use for. They're not raised for meat because they're not as cost effective to feed as beef cattle. Gotta keep getting the cow pregnant to keep making milk.
It's kind of funny, having the calves slaughtered to get the milk that is naturally meant for them is considered vegetarian (as long as you personally don't eat the veal).
If they're kept on abusive factory farms, that's still vegetarian.
When the dairy cows gets their throats slit because milk production drops below profitablity after ~5 years, the milk is still seen as vegetarian (as long as someone else buys the meat).
No matter how much death and suffering takes place at the farm, the milk is seen as vegetarian. But at rennet, that's where they draw the line.