I think that the third Triforce piece needs to be in "L3," since you can only unlock the gate to the outside Dark World with all three pieces. Once you unlock it, Zelda rushes ahead of you, (Not sure why yet...) and gets kidnapped. When you're exploring this Darkened World, Zelda will pop up occasionally and fool you with something. Each encounter brings you closer and closer to the realization that she's been twisted and perverted into a dark puppet. I'd guess there should be two brief encounters early on in the dark world, followed by one final encounter a few sceens before the miniboss where you fight and (Hopefully.) Heal Zelda.
Then, I'd suppose, Zelda snaps back into it and follows you back to the Lord Menace's castle.
Wait; .. perhaps it's not a castle. Perhaps it IS Link's House's equivalent! Perhaps Link's house is somehow a source of power that nobody knew about except Lord Menace, so he's using it to draw strength from. This probably means that Link's house will have to be expanded in the light world to accommodate such a thing. A 1x2 Fight. Ooh. :p When you beat his first stage, you advance to the second room (There's no door; just a scrolling screen transition.) and you fight the second and final phase.
