In a heavy saucepan melt butter over moderately low heat. Whisk in flour and cook roux, whisking, 3 minutes. Whisk in milk and simmer sauce, stirring, 8 minutes. In a bowl whisk eggs and add 1 cup sauce in a stream, whisking. Whisk egg mixture into remaining sauce and whisk in dill, nutmeg, and salt and pepper to taste. Keep bechamel warm, its surface covered with plastic wrap. Preheat oven to 375°F. In a kettle of boiling salted water cook pasta until just al dente. Rinse pasta in a colander and drain well. In a bowl stir together lamb and braising liquid. In a buttered 2-quart shallow baking dish spread half of pasta evenly and spread lamb mixture evenly over it. Top evenly with remaining pasta and pour bechamel over pasta. Sprinkle pastitsio with cheese and bake in middle of oven until bechamel is set, about 40 minutes.