Combine the mayonnaise, ketchup, mustard and vinegar in a bowl. Set aside.
Place one-third of the potato chips in a baking dish. Layer with one-third of the cheese, sauerkraut and corned beef. Add half of the remaining chips in another layer on top, then evenly layer half of the remaining cheese, sauerkraut and corned beef. Finish with the remaining chips followed by the rest of the cheese, sauerkraut and corned beef. Broil just until the cheese melts.
Toss the lettuce with the mayonnaise mixture and top the chips. Serve immediately.