Would you mind citing which kind of cheese you eat? Because much cheese has little to no lactose, and also goat lactose does not necessarily have the same effect as cow lactose. Finally, the fats and proteins in cheese affect digestion and possibly sugar absorption.
Honestly when battling sugar cravings it would be rather large chunks of parmesan cheese because I find it rather sweet. I assumed that was due to lactose but perhaps I'm wrong about that. It could also be that even a small amount of lactose tastes sweet after a while of not eating sugar.
Parmesan has close to zero lactose. However, it has an extremely high level of free glutamate, up to 1.6%, which is why it tastes delicious and makes other food taste delicious. Probably should avoid it, along with MSG, if you have blood pressure issues. Probably fine otherwise.
I do drink a lot of milk so I do know I'm not lactose intolerant so my prior assumption was that cheese wouldn't bother me either. I didn't know that hard cheese had so little lactose and I'm happy to be corrected. The parmesan cheese was thankfully just a transition phase that I was able to stop.