Combine cheeses; set aside.
Combine breadcrumbs and next 5 ingredients (breadcrumbs through turkey). Divide mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty.
Place patties on a grill rack coated with cooking spray; grill 5 minutes on each side. Sprinkle burgers evenly with cheese mixture. Cook 1 to 2 minutes or until burgers are done and cheese melts. Place buns, cut sides down, on grill rack; grill 1 minute or until toasted. Place 1 patty on bottom half of each bun; top each serving with 1/4 cup lettuce, 3 tablespoons onions, and top half of bun.