Bring a large saucepan of water to a boil. Cook orzo until just tender, about 8 minutes or according to package directions. Drain.
Meanwhile, cook lamb (or beef or turkey) in a medium nonstick skillet over medium heat, stirring, until browned, 2 to 3 minutes. Drain in a sieve set over a bowl. Clean and dry the pan.
Add oil to the pan and heat over medium heat. Add onion and cook, stirring, until softened, 3 to 5 minutes. Add garlic, cinnamon, rosemary (or oregano) and crushed red pepper (if using); cook, stirring, until fragrant, about 1 minute. Add the lamb (or beef or turkey) and tomato sauce; cook, stirring occasionally, until the sauce is thickened, 5 to 7 minutes. Remove from the heat and stir in olives, salt and pepper. Toss the orzo with the sauce. Serve garnished with feta.