Bring a large pot of well-salted water to a boil for the spaghetti.
For the meatballs: In a large bowl, add the lamb, pork, Parmesan, parsley, breadcrumbs, egg, garlic and some salt and pepper. Mix until combined; be sure not to overmix, so the meatballs stay tender. Form into 24 golfball-size balls; place on a large plate, and chill in refrigerator for at least 15 minutes to firm up, so the meatballs don't fall apart when seared.
For the sauce: Heat a large Dutch oven over medium-high heat. Add olive oil to coat the pan, then add the meatballs. Cook, turning occasionally, until browned on all sides, about 10 minutes. Transfer the seared meatballs to a plate. To the same pan, add the garlic and onion; saute until the garlic just begins to brown at the edges. Add the pureed tomatoes, oregano, some salt and pepper, and the meatballs. Reduce the heat to low and simmer until the meatballs are fully cooked, 30 minutes.
Add the spaghetti to the pot of boiling water, and cook according to package directions. Strain into a colander, then add the cooked pasta to tomato sauce, tossing everything together to coat the noodles. Garnish with freshly grated Parmesan, and serve.