Preheat the oven to 400 degrees F (200 degrees C).
Combine ground beef, ground lamb, onion, 3 tablespoons yogurt, olive oil, paprika, cumin, coriander, oregano, salt, and pepper in a bowl. Mix until very well combined and smooth.
Divide meat mixture among 4 rectangular sheets of parchment paper. Place a piece of parchment on top of the meat and use a rolling pin to spread it all the way to the edges in a very thin layer covering the sheet of parchment paper. Remove the top sheet.
Starting at the shorter end of the paper, fold the meat covered parchment, several times in about 1 ½-inch folds. Place folded filled parchment on a rimmed baking sheet.
Bake in the preheated oven for 30 to 35 minutes, draining off some of the accumulated fat and juices halfway through.
Unravel meat from the paper and return to the baking sheet. If you prefer more browning, return unfolded meat to the oven for 5 to 10 minutes longer. Sprinkle with 1 to 2 tablespoons lemon juice.
Meanwhile, combine remaining yogurt and lemon juice in a small bowl. Stir in garlic; season with salt. Add 1 or 2 tablespoons water if sauce seems too thick.
Tear meat into large pieces and serve on warm pita with parsley leaves, sliced onion, and tomato. Drizzle with yogurt sauce and hot sauce.
