Whether "true bechamel" uses nutmeg is kind of irrelevant. What is "true" bechamel anyway? Who decided? Is it the first bechamel? Is it some famous chef's bechamel? and if someone likes it with a "non standard ingredient" what are we to do? And what if the dish being made is not in the French tradition but is Greek or Italian? They all do bechamel in a different way. And we should be grateful or everyone would be making the same food in the same way and what would really be the point of cooking forums???!!!
Ada Boni, Talismano della felicita', one of the standard texts of italian cooking, gives nutmeg as one of the ingredients of besciamella (bechamel in italian). Artusi's "balsamella" doesn't. Many Italian besciamella/balsamella sauces have nutmeg. What do italians care about what the "real" bechamel is? Maybe it was invented in Italy, or in Greece, or who knows, maybe even in France. Maybe it was invented in each place (it doesn't take a culinary genius to make a sauce of butter and milk thickened with flour!) Maybe many housewives or personal chefs of ancient noblemen came up with the same or similar recipe over the years. (By the way did anyone know that Leonardo Da Vinci was the head of the kitchen (top chef) to Ludovico il Moro in Milan, and invented all these machines for use in the kitchen. He also, in his youth, he opened a restaurant with his friend. There's a hilarious account of this somewhere - i can try to find it. )
If you want to make lasagna with bechamel, then you want to put a little nutmeg. DO NOT expect ANY italian text to give you the quantity. Taste it. It's supposed to be subtle. They also put nutmeg in mashed potatoes by the way, and it's a very nice touch. Is there some big-ego famous chef that says "true mashed potatoes" have no non-standard ingredients? probably. Let them eat their own dishes done exactly the same way every time then.
As for exact quantities, i don;t know anyone here who makes lasagne with a written recipe - the cut off a chunk of butter, throw in some flour, let it bubble and then add milk, salt, nutmeg, maybe pepper. stir, cook. You can find a million recipes for bechamel. You probably would need about three cups of bechamel for a 13 X 9 pan.
I just looked in ada boni's book and there are many recipes for lasagne - some with bechamel, some with ricotta (also bechamel), some with neither and just slices of mozzarella, some with mushrooms. Every town probably has its recipe! It's not a cake, it won;t fall, it requires no engineering or chemistry, you can fool around with it till you like it.