Heat oil in a large nonstick skillet over medium-high heat. Add oregano and garlic; sauté 30 seconds. Add tomatoes, green onions, 2 tablespoons parsley, and lemon juice; cook 2 minutes or until thoroughly heated.
Combine tomato mixture, spaghetti, and 3/4 cup cheese; toss gently. Top with remaining cheese and parsley, and serve with pepper. Garnish with lemon slices and green onions, if desired.