In a medium bowl, whisk together oil, lemon juice, and oregano. Place lamb cubes in a large, shallow bowl, and pour marinade over lamb, tossing to coat evenly. Cover with plastic wrap, and let marinate in refrigerator 4 to 6 hours.Advertisement
Heat grill to medium. Remove lamb from refrigerator; season with salt and pepper. Thread two to three lamb cubes on each skewer; place on a parchment-lined baking sheet. Brush grill with oil.
Working in batches, grill until lamb is charred on the outside but still pink inside, 3 to 5 minutes per side, depending on heat of grill. Transfer to a platter. Serve hot with feta cheese on the side.
Soak bamboo skewers in hot water for one hour to keep them from scorching on grill.