Cook bacon in a large, deep skillet over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain on a paper towel-lined plate.

Preheat an outdoor grill for medium-high heat and lightly oil the grate. Evenly coat salmon with olive oil.

Cook on the preheated grill, skin-side down, about 5 minutes; flip and cook on other side until skin easily lifts off flesh, about 5 minutes more. Flip again; continue cooking until salmon flakes easily with a fork, 2 to 3 minutes more.

Whisk mayonnaise, dill, and lemon zest together in a small bowl; divide and spread onto 2 toasted bread slices. Top each with 1 portion salmon, 2 tomato slices, 2 bacon strips, 1 lettuce leaf, and 1 remaining toasted bread slice.