Preheat a grill to medium. Place the bacon in a large bowl, crumble the beef on top and season with salt and plenty of pepper; toss well. Shape the meat mixture into four 3 1/2- to 4-inch patties.
Using a serrated knife, trim the bun tops and bottoms so they will sit flat on the grill. Spread the mayo and ketchup on the insides of both halves; divide the cheese among the bottoms; cover with the tops.
Place the patties and cheese-filled buns on the grill, with the buns over a cooler area; cover the grill and cook for 2 minutes. Flip the patties and buns, cover and cook until the patties are medium, both sides of the buns are toasted and the cheese is melted, about 2 minutes. Transfer the buns to plates and open carefully. Place a patty, a tomato slice and some lettuce on each bun bottom; replace the bun tops.