Combine 1/4 cup yogurt, cucumber, garlic, and 1/4 teaspoon pepper in a small bowl; set yogurt mixture aside.
Combine remaining 2 tablespoons yogurt, remaining 1/4 teaspoon black pepper, 1/3 cup panko, bell pepper, onions, dill, rind, juice, salt, and egg white in a medium bowl. Gently stir in crab. Divide crab mixture into 4 equal portions (about 1/2 cup each), shaping each into a 3/4-inch-thick patty. Place remaining 1/3 cup panko in a shallow dish. Dredge patties in panko.
Heat a large skillet over medium heat. Add oil to pan; swirl to coat. Add patties; cook 3 minutes on each side or until golden. Top each bread slice with 1 lettuce leaf, 1 patty, and about 2 tablespoons reserved yogurt mixture.