Heat the bacon grease and vegetable oil in a large skillet over medium heat. You want about a ½” of oil/grease mixture in the bottom of your pan.
Slice the tomato about ⅓” thick. Whisk your egg in a medium bowl and pour whisked egg into a shallow bowl or dish. Place the cornmeal in another shallow bowl or dish and mix in a bit of salt and pepper with a fork. Dip each slice of tomato into the egg, coating both sides, and then dredge both sides in the cornmeal mixture. Place each tomato slice into the heated oil in the skillet and brown on each side. As each slice is done, drain it on a paper towel.
While you are frying your tomato slices, begin warming your braised bacon slices. In a medium skillet, heat the slices gently over medium-low heat until warmed through. Hold in the warm pan until ready to put into the sandwich.
Toast your bread slightly and then spread mayonnaise on one slice of the bread, then layer your lettuce leaves, warm braised bacon, and crispy fried tomato slices on the first slice of bread, topping with the second slice of bread. Serve immediately.