Hi Dizzydi, I had my gallbladder removed years ago before I was diagnosed Diabetic, I used to follow the low fat diet again before I was diagnosed
When you say you can't drink milk is that because you are lactose intolerant or that you don't like it, I use low fat milk because I don't like the creamy taste of full milk.
However I do the low carb diet but have tweaked it to contain enough fat, in that I've gone from low fat butter to full fat butter, I have double cream in coffee, use butter to fry my eggs, however its up to you and how much fat you can stomach without the inevitable consequences of frequent visits to the loo, all I can say is try a bit then if ok add a bit and so on.