Theory: The Lost Levels' Location

Abstract
Super Mario Bros.: The Lost Levels/Super Mario Bros. 2 (JP) takes place within the “Special Worlds” from Super Mario 3D Land.

Arguments

 * Argument 1: The story of Super Mario Bros.: The Lost Levels is almost identical to the story of Super Mario Bros., with the key difference being that Lost Levels is said to be set in a "parallel world" to it. The same description of a “parallel world” could be applied to the 8 Special Worlds of Super Mario 3D Land. It is a familiar, yet different world accessed through a special Warp Pipe. The World Maps of Special 1-Special 7 are warped versions of World 1-World 7, similar to the World Map of Super Mario Bros.: the Lost Levels being the same as the World Map seen in Super Mario Bros.


 * Argument 2: the 8 Special Worlds are intended to be a challenge for the player, often remixing elements and stages found in the first 8 Worlds for its levels. This is another similarity they share with Super Mario Bros.: The Lost Levels, which mostly reused elements from Super Mario Bros., but with a twist of harder difficulty. It even once went by the name “Super Mario Bros.: For Super Players” in Super Mario Bros. Deluxe.


 * Argument 3: throughout the Special Worlds, Dry Bowser appears as an antagonist, despite the fact that Bowser was not seen transforming into Dry Bowser during the game and that he appears in his regular form later on. Perhaps this “Dry Bowser” is supposed to parallel (or be) the second Bowser seen in Super Mario Bros.: The Lost Levels (often called Blue Bowser or Bowser’s Brother).


 * Argument 4: After clearing Special 1-Castle in Super Mario 3D Land, Mario saves Luigi from Dry Bowser, allowing the player to play as Luigi from that point onward, with his special higher & further jumps and less traction. While this has little meaning in-universe, this could be a real world nod to the fact that Luigi is selectable as a playable character in Super Mario Bros.: The Lost Levels, where his higher & further jumps and less traction were first introduced.


 * Argument 5: The Poison Mushroom, which was introduced in Super Mario Bros.: the Lost Levels, made its grand return to the Super Mario series after 25 years in Super Mario 3D Land, exclusively appearing in the Special Worlds.