Combine the mayonnaise, garlic, the zest and juice of 1 lime, the dill and parsley in a small bowl. Cover and refrigerate.
Cook the bacon in a large skillet over medium-high heat until crisp. Break the slices in half.
Preheat a grill or grill pan to medium high. Slice the salmon on the diagonal into 8 thin pieces. Season the salmon and red onion slices with salt and pepper and rub with the olive oil. Sprinkle with the zest and juice of the remaining lime. Grill the red onion slices, turning occasionally, until tender and charred, about 5 minutes. Grill the salmon until marked and just cooked through, turning once, 1 to 2 minutes.
Lay out 4 slices of toasted bread; top with some of the herbed mayonnaise, a lettuce leaf, a piece of salmon, some tomato and avocado slices and 2 bacon halves. Top each with a piece of toast, then repeat the layering (mayonnaise, lettuce, salmon, tomato, avocado and bacon). Spread the remaining 4 bread slices with herbed mayonnaise and place on top of the sandwiches. Secure each sandwich with 4 toothpicks and cut into quarters.