Cheddar cheese is an example of a cheese with no — or almost none, in some cases — lactose. Hard cheeses, such as cheddar and parmesan, and aged cheeses tend to contain little or no lactose in them naturally.
Very few types of cheese have lactose in them by the time the milk is finished being processed. This is because milk is converted to cheese in a fermentation or souring process known as acidification. After this process, the lactose in the cheese is turned into lactic acid, which is entirely different from lactose. Fresher cheeses are made of milk that may not have had a chance to ferment completely, so they may contain some lactose.