Preheat the pellet smoker to 275°F. Set it up for indirect cooking, and lightly oil a small rimmed baking pan.
In a large bowl, combine the ground lamb, breadcrumbs, egg, feta, red onion, garlic, parsley, oregano, salt, and black pepper. Mix gently until just combined to help keep the meatloaf tender.
Shape the mixture into a compact loaf in the prepared pan. Place the pan in the smoker and cook until the center reaches 160°F on an instant-read thermometer, about 1 hour to 1 hour 20 minutes. Rest the meatloaf for 10 minutes before slicing.
While the meatloaf cooks, stir together the Greek yogurt, squeezed cucumber, and lemon juice in a small bowl. Refrigerate the tzatziki until ready to serve.
Warm the pita breads on the smoker for 1 to 2 minutes per side, just until soft and heated through. Serve them with slices of lamb meatloaf and the chilled tzatziki.