In a mixing bowl, combine the ground lamb, oregano, garlic powder, cumin, salt, and pepper until evenly incorporated.
Form the meat mixture into thin rectangular patties approximately 1/2 inch thick.
Heat a large non-stick skillet over medium-high heat and sear the patties for 4 to 5 minutes per side until browned and the internal temperature reaches 160 degrees Fahrenheit.
Prepare the dressing by whisking together the Greek yogurt, lemon juice, and chopped dill in a small bowl.
Divide the chopped Romaine lettuce into two serving bowls.
Top the lettuce with cucumbers, cherry tomatoes, red onion, and Kalamata olives.
Slice the cooked gyro patties into strips and place them over the vegetables.
Garnish with crumbled feta cheese and serve with the yogurt dressing.