Melt butter in a small saucepan over medium- low or low heat.
Whisk in the flour until blended with no lumps. Cook and stir 1 minute, while you heat the milk for 15-30 seconds in a glass measuring cup in the microwave.
Stir or whisk warm milk, dill, salt, pepper, and nutmeg into the butter/flour mixture. Cook on low, uncovered, stirring frequently for about 5 minutes, or until it's thick enough for you. Remove from heat and keep warm until ready to serve, or reheat over low heat. Before serving, squeeze juice from half a lemon into the sauce and stir to blend, reheating if necessary.
Drizzle about 1-2 tablespoons warm sauce over a piece of grilled, poached or pan-seared salmon.