Step 1Combine 1/2 cup of the oil, the lemon juice, garlic, oregano, salt and pepper to taste in a bowl and toss in the lamb cubes. Cover and refrigerate for at least 1 hour and up to 3 hours.
Step 2Heat the grill to medium-high or the broiler.
Step 3Alternately thread the meat, peppers, onions, tomatoes and bay leaves onto the skewers. Brush the skewers with the marinade. If broiling, place the skewers on a rack over a pan to keep the juices from dripping into the oven and broil about 4 inches from the heat source or place the skewers on the grill. Brush occasionally with a little of the marinade. The souvlaki will need about 6 to 7 minutes per side for rare, about 8 to 10 minutes for medium, and about 12 for well-done.
Step 4While the skewers are cooking, lightly brush the pita bread with some of the remaining 3 tablespoons of oil and either pan-fry lightly, preferably in a cast-iron skillet over medium-high heat, or place on a cast-iron griddle or directly on the grill rack. Turn, brush the other side with the oil and grill lightly, 1 to 2 minutes total. The bread should not toast, but rather should be soft and pliant.
Step 5Serve the souvlaki on the skewer over the bread, accompanied if desired with Tzatziki and Greek Pan-Fried Potatoes.