Sprinkle meat with 1 teaspoon salt and 1/4 teaspoon pepper; place in bowl.
Cover; marinate 3 hours or overnight in refrigerator, stirring several times.
Meanwhile, partially cook onions in large amount boiling salted water for 5 minutes; drain.
Arrange lamb cubes, onions, and green pepper pieces alternately on long skewers.
Brush with oil.
Grill over hot coals till lamb is desired doneness, turning and basting with oil occasionally.
Allow 10 to 12 minutes for medium-well.