Here is a thought experiment:
If you eat only cheese for a week, zero carbohydrate cheese, and no protein. What will happen?
There is one theory that without protein or carbs to spike the insulin the fatty acids are not uptaken by the adipocytes, and you wont gain weight during the week long festival of cheese. Is this mechanistic theory credible?
Cheese is dairy, lactose is sugar.
https://amycookseats.com/how-much-sugar-in-american-cheese/
Many cheeses have very little lactose.
It does vary by cheese, but some not only have the lactose, but added sugar as well. American Cheese for example.