Start by making your lemon-caper mayo. In a bowl of a food processor, combine scallions, capers, parsley, lemon juice, lemon zest, and mayonnaise. Pulse a few times until everything is combined well. Season with salt and pepper to taste and transfer to small bowl.
Light a charcoal grill under medium high heat. Rub small amount of olive oil onto salmon fillets. Season with salt and pepper. Spread desired amount of lemon mayo on salmon fillets. Grill salmon fillets, skin side down first, on direct heat for about 3-4 minutes per side.
To assemble sandwiches, place a good amount of leftover lemon mayo onto bottom slice of toast. Place lettuce leaf atop mayo and add salmon fillet. Top with tomato and 3 sliced of bacon. Close sandwich with remaining piece of toast and enjoy!