In a mixing bowl, combine olive oil, minced garlic, lemon juice, cumin, coriander, cinnamon, paprika, and salt. Mix well and coat the lamb slices. Marinate for at least 4 hours or overnight.

Heat a large skillet or grill pan over medium-high heat. Cook the marinated lamb in batches, searing until golden and slightly charred on the edges.

For the garlic sauce, mix Greek yogurt, tahini, and a pinch of salt in a small bowl.

Warm the flatbread and spread a layer of garlic sauce over each piece.

Add the cooked lamb slices, followed by cucumbers, tomatoes, and pickled turnips.

Roll the wraps tightly, slice in half, and serve immediately.