To make a bechamel for lasagna, blend a roux with any kind of liquid dairy, any type of substitute dairy liquid or a non-dairy liquid, such as vegetable stock. A bechamel is a basic white French sauce whose ingredients do not change based upon how you use the bechamel, although individual chefs and culinary experts often incorporate slight variations into their interpretation of the classic French bechamel.
For a basic bechamel sauce, melt 1/2 stick of butter in a heavy saucepan until bubbly. Sprinkle 1/4 cup of cake flour or all-purpose flour into the butter. Stir continuously until the butter adopts a slightly golden tint. Over medium heat, whisk vigorously while slowly pouring in 3 cups of milk until the mixture begins to thicken.
Add 1/8 teaspoon of freshly ground nutmeg, and salt and pepper to taste. Cook the mixture for about 15 minutes, whisking. It should be thick and smooth, and it should coat the back of a spoon. Alternatively, add 1 small diced onion and 2 chopped cloves of garlic to 5 tablespoons of melted butter, 1/3 cup of flour and 4 1/2 cups of milk to make a large quantity of bechamel for any use.
For a thicker or thinner bechamel, use flour and butter in a 1:1 ratio, such as 1 tablespoon of flour and butter for a thin bechamel, 2:2 for a medium bechamel, 3:3 for a thick bechamel and 4:4 for a heavy bechamel.