In a bowl, toss lamb cubes, cumin, coriander, paprika, turmeric, minced garlic, lemon juice, olive oil, salt, and pepper. Marinate for at least 2 hours or overnight.

Warm a large cast-iron skillet over medium-high heat for about 3 minutes. Add a drizzle of oil.

Add marinated lamb in a single layer. Cook for 8–10 minutes, turning occasionally.

Transfer lamb to a plate and let it rest for 5 minutes.

In a bowl, whisk Greek yogurt, mayonnaise, crushed garlic, lemon juice, and olive oil until smooth; season with salt and white pepper.

Warm pitas, spread garlic sauce, layer lamb, veggies, herbs, and pickles. Roll tightly and serve immediately.