Melt the butter in a big frying pan or a wide pot. When it's bubbling add the flour.
Mix the butter and flour with a wooden spoon until they form a thick paste. Cook, stirring, for about a minute over low heat. Don't let the paste brown (it should be yellow in color).
Add about 1/3 cup of milk and whisk vigorously until the milk has been completely absorbed by the flour-butter paste.
Keep adding the remaining milk, in 1/3-1/2 cup amounts. Whisk thoroughly after each addition and wait until the milk is combined with the sauce. Mix vigorously especially at the beginning, to make sure that no lumps form.
Cook the sauce for 2-5 minutes on the lowest heat until thickened. Keep in mind that the sauce will still thicken after taking the pot off the heat.
Remove the pot from the heat. Season with salt, pepper, nutmeg and lemon juice (if using). Use immediately.