In a medium skillet over medium heat on the stovetop, arrange the bacon in one layer. Cook until golden brown and crisp, 8 to 10 minutes. Transfer the bacon to a plate lined with paper towels to drain.
Prepare the grill for direct cooking over medium heat (350° to 450°F). Preheat the griddle over direct medium heat for 5 minutes.
Prepare the grill for direct cooking over medium (400°F). Preheat the griddle over direct medium heat for 5 minutes.
Lightly butter one side of each bread slice. Flip the slices and generously spread some of the mayo on each slice. Arrange a layer of lettuce on 2 slices. Top with the tomatoes, turkey, and the bacon. Close the sandwiches, mayo-side down.
Place the sandwiches on the griddle and grill, with the lid closed, until the bread is toasted, 2 to 3 minutes. Using a spatula, flip the sandwiches and grill, with the lid closed, until the bottoms are toasted, 2 to 3 minutes more. Serve at once.
