Future World has 4 floors which are done in succession without any checkpoint between them.
Unlike other lobbies, this one has a potion shop.
Health Potion cost 4 diamonds and Stamina Potion cost 1.
You are able to purchase the two Game Over shop heart pieces here if you haven’t bought them already.
You have to re-enter the room for the 2nd heart piece to appear, just like with the Game Over shop.
Future World does not have a Boss Door or Boss Key and instead adds a warp pad to the lobby, allowing you to teleport between the boss room entrance and lobby.
Because of this there is no foreseeable way of skipping the dungeon floors like with other dungeons.