Heat the oven to 400°F (200°C). Check that your parchment is rated for this temperature. Put a rack in the center and set out a rimmed baking sheet.

Mix the beef, finely grated onion, garlic, 60 g (1/4 cup) yogurt, paprika, cumin, oregano, salt and pepper until evenly combined and slightly tacky. Divide in half.

Place one half on a 12-by-16-inch parchment sheet, cover with another sheet and roll to an even layer about 1/8 inch (3 mm) thick, leaving a small margin. Remove the top sheet. Starting at a short edge, roll the bottom parchment and meat together so paper separates the layers. Repeat with the second half.

Put both rolls seam-side down on the rimmed baking sheet. Bake about 25 minutes, then carefully insert a thin instant-read thermometer through the end into the meat at the center. Continue cooking until the ground beef reaches at least 160°F (71°C); time is a guide, not the doneness test.

While the meat cooks, stir the remaining 120 g (1/2 cup) yogurt with lemon juice. Refrigerate until serving. Warm the pita following its package instructions.

Open the cooked rolls carefully, letting steam escape away from you. Remove all parchment and tear the meat into strips. Transfer meat with a small amount of its rendered juices to a large skillet over medium-high heat. Cook in a single layer for 2 to 4 minutes, turning once, until some edges brown. Work in batches if needed.

Divide the beef, yogurt sauce, tomatoes and cucumber among the four pita breads. Serve promptly.