Preheat the broiler. Open the hamburger buns and arrange on a baking sheet. Brush the buns all over with 1 tablespoon of the mayonnaise. Toast until golden on both sides, 1 to 2 minutes per side. Cut into very small pieces and set aside.
Combine the cheese, 1/2 cup mayonnaise and a pinch of salt in a food processor and process until very smooth. Transfer to a bowl, cover and refrigerate until ready to use.
Whisk the remaining 1/2 cup mayonnaise, the ketchup and mustard in a bowl for the sauce, cover and refrigerate until ready for use.
Arrange the bacon in a large nonstick skillet (do in batches if necessary) and heat over medium heat. Cook until golden brown and crispy, 4 to 5 minutes per side. Remove, let cool slightly and chop into small pieces.
Wipe out the skillet. Heat the oil in the skillet over medium-high heat. Add one-third of the onion and cook, stirring frequently, until soft and just beginning to brown, about 4 minutes. Add the ground beef, 3/4 teaspoon salt and a few grinds of pepper. Cook, stirring and breaking up into smaller pieces, until browned and cooked through, about 4 minutes. Stir in a 1/3 cup of the prepared ketchup sauce and cool the beef mixture to room temperature.
Let the cheese mixture soften at room temperature, about 30 minutes, before building the dip. Layer the dip in a medium, straight-sided 3-quart clear glass trifle bowl or your favorite serving dish. Spread out the cheese mixture and then top, in even layers, with the buns, tomatoes, beef, the remaining ketchup sauce, the pickles, the remaining onions and the bacon.
Wrap and refrigerate until chilled, at least 1 hour and up to overnight. Top with the shredded lettuce right before serving. Serve with chips for dipping.