Most cheeses don't contain lactose! What's happening when milk turns to cheese is a souring process called acidification, whereby the lactose in milk is converted into lactic acid. This is the magical fermentation process in cheesemaking, when a sugar — in this case, milk sugar, or lactose — is converted into something else — in this case, lactic acid, which happens to be an entirely different entity from lactose. By the time a cheese is made, most or all of the lactose that had been present in the milk no longer remains.
The longer that milk is left to sour, the greater the opportunity for all of that lactose to dissipate into lactic acid. A longer period of acidification allows the protein chains to form even stronger bonds, which will result in a firmer curd — and ultimately a firmer cheese that can age longer. Therefore, it's the harder, drier, and more aged cheeses that will be the safest to eat if you're lactose intolerant. Fresher cheeses that are higher in moisture may retain a small amount of lactose because the milk has not been left to ferment completely. People who are lactose intolerant may have issues with fresher styles.
If you don't really know if you're lactose intolerant, try eating a hard cheese like parmesan, which has virtually no residual lactose. No good? What you probably have then is a MILK allergy, in which case all types of cheese will give you problems. But if harder, (virtually lactose-free) cheeses are okay but you still have issues with fresher, high-moisture cheeses plus yogurt, ice cream, and other dairy products, then it's probably safe to say that you are indeed lactose intolerant.
If you're unsure, take the time to figure it out. It will make us cheesemongers all the more happy to serve you.
Nora Singley is an avid lover of cheese, and for some time she was a Cheesemonger and the Director of the Cheese Course at Murray's Cheese Shop in New York City. She is currently a chef on The Martha Stewart Show.