On a board, weave 3 bacon half-strips horizontally and 3 vertically into a flat square. Repeat with the remaining 6 half-strips to make a second square, then transfer carefully with a wide spatula to a cold 12-inch skillet.
Cook over medium-low heat for 8 to 10 minutes, pressing briefly with a smaller heavy pan during the first 2 minutes to keep the bacon flat. Remove the press, turn the squares carefully and cook for 6 to 8 minutes more until crisp throughout; drain on a rack.
Lay tomato slices on paper towels, sprinkle with salt and let drain for 10 minutes, then blot dry. Refrigerate drained bacon on a plate for about 20 minutes until cold before assembly; the prep time includes cooling.
Spread mayonnaise over one face of each bread slice. Lay one dry lettuce leaf on each face, then divide tomato slices over 2 of the slices and season with black pepper.
Place one cooled bacon square over each tomato layer and close with the remaining bread and lettuce. Cut across the middle and serve cold or refrigerate at 40°F or below, packing with ice packs for lunch.