In a medium bowl, combine garlic, spices, lemon juice, and 3 tablespoons olive oil. Season with salt and black pepper, to taste, and whisk to combine.
Place chicken thighs in a large, zip-to-lock plastic bag and pour marinade mixture on top. Seal the bag and thoroughly coat chicken. Refrigerate for several hours to overnight.
To prepare the yogurt sauce, combine all ingredients in a glass or other non-reactive bowl and stir to combine. Cover and refrigerate at least 1 hour.
Heat remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Remove chicken from bag and discard remaining marinade. Add the chicken to the hot skillet and brown on each side, approximately 2 minutes per side.
Reduce heat to medium and continue cooking until chicken is cooked through, approximately 6-7 minutes per side. Remove from heat and let cool for several minutes.
Slice chicken and arrange on lettuce leaves. Top with tomatoes and cucumbers and Greek yogurt dressing.