To prepare the marinade, combine the oil, garlic, oregano and thyme in a large zip-close plastic bag; mix well. Add the lamb, seal the bag, and turn several times to coat. Marinate the lamb at room temperature 30 minutes or refrigerate overnight.
Preheat the broiler. Spray a broiler pan with nonstick spray; set aside.
Thread 5 lamb cubes, 2 onion wedges, and 2 bell pepper pieces onto each of 6 (12-inch) metal skewers, alternating the ingredients. Transfer the skewers to the broiler pan.
Broil the skewers 4 inches from the heat, turning at least once, until the vegetables are tender and the lamb is cooked through, 8 to 10 minutes. Serve with the rice.