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Combine all the ingredients for the marinade in a bowl and toss in the lamb cubes. Cover and refrigerate for at least one hour and up to three hours.
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Light the grill or preheat the broiler.
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Thread the meat, peppers, onions, tomatoes, and bay leaves onto the skewers, alternating between each. Brush the skewers with the marinade.
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Grill the souvlaki about four inches from the heat source if cooking under a broiler or slightly less if grilling on a barbecue. If doing
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this under a broiler, place the skewers on a rack over a pan to keep the juices from dripping into the oven. While grilling or broiling, brush occasionally with a little of the marinade. The souvlaki will need about six to seven minutes per side for rare, about eight to nine minutes for medium, and about 10 for well-done.
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While the skewers are cooking, brush the pita bread with 1 teaspoon of olive oil and either pan fry lightly, preferably in a cast-iron skillet or over a cast-iron griddle, or directly on the barbecue rack. Turn, brush the other side with oil and grill lightly. The bread should not toast, but rather should be soft and pliant.
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Serve the souvlaki on the skewer over the bread, accompanied if desired with tzatziki and Greek pan-fried potatoes.
