However (a big yay!), cheesemaking is all about ridding milk of lactose. When milk is made into cheese, the lactose sugar converts to lactose acid. The older the cheese, the less lactose. Parmesan and old, crusty goudas? Hardly any lactose to speak of. And sometimes even young cheeses (especially ones left to acid-set over night) have had much of their lactose leeched off when the curds (proteins, solid matter) are separated from the whey (the liquid).
So if you think you might be lactose-intolerant, try cheeses with less lactose — the aged ones. Most of the lactose should have morphed into lactic acid by the time it gets to you.