Yes that is possible. I think it depends on how well the lactase works to aid the digestion. I have mixed results from it. But then many people have problems digesting more than just lactose in dairy. It's often a mix of lactose, casein, whey, etc. that make digestion so difficult.
But you can get all those vitamins and nutrients from other sources, such as leafy green veggies (spinach, etc.). As for the fats, you can get healthier fats from things like olive oil, grape seed oil, etc.