Lactose plays a role in cheese making as it is fermented by bacteria.

I'm not looking for a cheese alternative. I want the exact same cheese as it is now, just without the need for a cow. So it better have lactose.

Casein is the primary protein in milk, and it has a ton of uses. Humans have been consuming animal milks for a very long time, and milk is a key ingredient in a lot of food. Baking, emulsifying, cooking, fermenting, it's the casein that makes the milk magic.

Some people can be allergic to casein, but far more lack the digestive enzyme to break down lactose. Lactose is what the yeast and bacteria ferment with in cheese and yogurt, but casein is the protein that holds it all together. Conceivably, you could use a different sugar and still get something that sort of resembles cheese and yogurt, but you have a much harder time replacing the casein.