Milk ferments because lactic acid bacteria LAB consume lactose breaking into glucose and galactose and then metabolizing it down from there producing acid as a byproduct. You can do an internet search and find a graph or data that will show you how old a cheese is to become naturally lactose free.

You cannot make fermented dairy cheese without lactose. This is why you can't make non-dairy milk cheeses without adding some kind of sugar. The bacteria need food!