Trim any excess fat from the lamb leg and slice it into thin, bite-sized strips.
In a medium bowl, combine the cumin, coriander, cinnamon, turmeric, sea salt, and black pepper, then toss the lamb strips until they are thoroughly coated in the spice blend.
Prepare the garlic sauce by whisking together the Greek yogurt, minced garlic, and lemon juice in a small bowl until smooth.
Heat the olive oil in a cast-iron skillet over medium-high heat and sear the lamb for 4-5 minutes, stirring occasionally, until browned and cooked through.
Lightly toast the whole wheat pita in the same skillet for 30 seconds per side until warm and pliable.
Assemble the shawarma by filling the pita with the spiced lamb, diced cucumber, tomato, and sliced red onion.
Finish by drizzling the creamy garlic sauce over the top and serve immediately.