Heat the oil and butter in a large skillet over medium-low heat until the butter melts. Add the onions, salt, and pepper. Cook, stirring occasionally, until very soft and browned, about 45 minutes. Let cool.

In a mixing bowl, combine the mayonnaise, sour cream, lemon juice, and hot sauce. Stir in the onions and taste. Add more salt, pepper, or hot sauce if desired. Refrigerate until cold, at least 2 hours. (Can be made up to 2 days ahead. Store, covered, in the refrigerator.) Serve with chips or sliced vegetables.