Season the meat generously with salt and pepper, then let it rest and come to room temperature.
Heat the gas or charcoal grill to a level of medium high heat. Thread the skewers, preferably stainless steel, with a pattern of 2 pieces of meat, 1 chunk of onion, and one pepper, repeated. Or any pattern you like. Or no pattern at all. Just be sure not to thread the meat and vegetables too tightly, to give them room to cook fully and to enjoy more the grilled surface area.
Brush the meat and vegetables with olive oil. Place on the grill and for medium-rare meat, cook for 10 minutes with the top on, then flip with tongs and grill another 10 minutes, top on. Remove from the heat and let the skewers rest for 10 minutes.
Remove the hot meat and vegetables from the skewers by pushing them off with a fork. Best not to serve the skewers, even small ones--it's awkward and difficult to remove the meat on the plate.
Notes
Storage and Reheating
Like most grilled meats, grilled lamb tastes the best hot off the grill or even at room temperature shortly after grilling. Store leftovers in an airtight container in the refrigerator for up to 4 days or in the freezer for up to 1 month (but frozen grilled meat can lose a lot of tenderness and juiciness; not recommended!). Reheat the meat by bringing it to room temperature, then searing in a skillet with extra virgin olive oil at medium high very briefly, just a minute or two.
Lamb Marinade Variation
You can easily change this up by marinating the cubed lamb ahead of time. Marinade ingredients would be simple too: the juice of 2 lemons, 2 garlic cloves cut in thin slices or 2 teaspoons garlic powder, 2 teaspoons of salt and a few grinds of black pepper. Toss to coat and allow to marinate for as little as 30 minutes and up to one day (refrigerated).