It's challenging, but do-able. The good thing about avoiding dairy products is that you never, ever have to diet!
No cheese, milk, cream or cakes that have butter. It's really not so bad and there are plenty of cookbooks for lactose-intolerant recipes.
Substitute for milk in making bechamel: powdered almonds blended with fresh water and a dash of salt and sugar. Then put it in a saucepan to boil with a tablespoon full of flour until it thickens to the consistency of thick cream. Pour it over sliced aubergines, sliced tomatoes and some cooked pasta and there you go. It's delicious and crisps up nicely in the oven.