Preheat oven to 425°F. Place a roasting rack in a medium-size roasting pan; set aside. Stir together oil, lemon juice, garlic, oregano, salt, and pepper in a small bowl until combined. Rub oil mixture evenly over lamb. Place lamb on rack in prepared pan. Pour tap water into bottom of pan until bottom is just covered (about 2 cups). Cover tightly with aluminum foil. Bake in preheated oven for 45 minutes. Remove foil, and reduce oven temperature to 375°F. Bake until a thermometer inserted in thickest portion of lamb registers at least 145°F, 45 to 55 minutes. Remove from oven; cover loosely with foil, and let rest 30 minutes. Remove lamb from rack, and place on a cutting board, reserving juices in roasting pan. Slice lamb into thin (⅛- to ¼-inch-thick) slices.
Divide lamb slices evenly among pita rounds; top each evenly with Tzatziki Sauce, red onion, cucumber, and tomato.
