Pulse the bacon in a food processor, or chop with a knife, until ground. (If using a knife, freeze the bacon for a bit first to make the chopping easier.)
Combine the bacon and beef in a bowl, mixing lightly. Divide the mixture into four equal portions. Gently flatten into 1-inch patties and make a thumb-size divot in the middle of each.
Heat a griddle or large cast-iron pan over medium-high heat. Evenly sprinkle the patties all over with salt and pepper. Griddle the burgers, turning when the bottom forms a dark brown crust, about 4 minutes. Add 1 ounce of cheese on top of each burger and cook for 2 minutes. Cover the pan and turn the heat off. Allow to sit, covered, until the cheese melts, about 1 minute. Place the burgers on the buns and top with lettuce and tomato. Cover with the top buns and serve.