Heat the olive oil in a large pan over medium heat. Add the lamb, salt, and pepper and brown the meat on all sides for about 5 minutes. Add the onions and allow to cook for another 10 minutes, stirring every few minutes to cook the lamb evenly. Add the water, tomatoes, and tomato paste and stir until the tomato paste has dissolved into the liquid. Bring the heat down to it's lowest setting and allow it to simmer, uncovered for 1 and 1/2 to 2 hours, stirring every 20 minutes.

During the last 30 minutes of cooking, preheat the oven to 350 degrees Fahrenheit. Bring about 5 cups of water to a boil in a medium-sized pot and add the orzo noodles. Boil them until they're nearly done, about 10 minutes, stirring every couple minutes to keep them from sticking to the bottom of the pot. Drain them and rinse quickly with cold water to keep them from cooking further.

Empty the noodles into a roughly 9 x 13 inch casserole dish. Remove the lamb mixture from the stovetop and empty it into the casserole dish, then stir it up until the lab mixture is evenly distributed throughout the orzo noodles. Place the pan in the oven and bake for 15 minutes. Remove it from the oven and serve alongside the Parmesan or mizithra cheese for sprinkling.