In a large saucepan, heat the olive oil over medium-high heat. Add the onion and garlic and cook, stirring, until translucent, about 5 minutes. Add the lamb and cook, stirring, until the meat is lightly browned, about 10 minutes. Spoon out the fat and discard.
Stir in the tomato paste, wine and oregano; season with salt and pepper. Cover and simmer over low heat for about 10 minutes. Add the spinach and mint; stir until wilted.
Meanwhile, in a large pot of boiling, salted water, cook the pasta until al dente. Drain the pasta, reserving ½ cup of the cooking liquid.
Toss the pasta with the cooking liquid and the ground lamb sauce.