Heat oil in large skillet over medium-high heat. Add onion and garlic; saute until onion softens, about 5 minutes.
Add lamb; cook until brown, breaking into small pieces, about 8 minutes.
Stir in tomatoes with juice, mint, ras-el-hanout, tomato paste, 2 1/2 tsp cumin, and cinnamon. Bring to boil. Reduce heat to medium-low. Simmer until lamb mixture is thick, stirring often, 15 to 18 minutes. Season with salt and pepper.
Meanwhile, bring 2 cups milk to simmer in medium saucepan. Remove from heat; cover to keep warm. Melt 6 Tb butter in heavy large saucepan over medium heat. Add flour; whisk until smooth. Reduce heat to medium-low; cook until roux is pale golden, whisking often, 3 to 4 minutes. Gradually add warm milk to roux, whisking until sauce is smooth.
Whisk 1 cup milk and 3 egg yolks in medium bowl; whisk into sauce. Whisk in feta and 1/2 tsp cumin. Bring sauce to boil, whisking often. Reduce heat to medium-low; simmer until slightly thickened, mashing with potato masher to break up cheese, about 5 minutes. Season sauce with salt and pepper. DO AHEAD: Can be made 1 day ahead. Cover; chill. Rewarm over low heat, whisking often, before using.
Preheat oven to 400°F Butter deep 14-cup (we used 9x13") baking dish. Cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain pasta; return to same pot. Mix 2 Tb butter into pasta. Add egg whites and 1/4 cup Parmesan; stir to blend.
Spread 4 cups pasta in dish. Spread lamb mixture over. Top with remaining pasta. Spoon sauce over; sprinkle with 1/4 cup Parmesan. Place dish on rimmed baking sheet. Bake pastitsio until heated through, about 40 minutes. Let stand 5-10 minutes.