The following thread contains spoilers for A Link Between Worlds.

What do you think the Lorule versions of other Zelda games would be like? Remember, not everything is the opposite in Lorule, it's just an alternate universe where everything is purple.

To start us off, in my headcanon, Lorule's Triforce was only destroyed on the Downfall Timeline, in their version of the Imprisoning War.

I have a lot of Lorule Headcanons.

(Also, I agree with that headcanon of yours, about the Imprisoning War.)

Lobule Adult Timeline Headcanon 1: Lorule!Wind Waker features a massive desert. Ravio's quest is to restore the oceans and ensue that the people of Lorule can be saved. He's accompanied by Kutora, a Sand Pirate Captain, her Lieutenants Dust and Hound, and the rest of the crew of the Tazm'l, which is her Sand Ship (Basically a Magitech Sand Crawler).
It's not an exact reversal of Hyrule, since the Great Flood still happens; it merely happens much later on, and Ravio ensues that everyone's on high ground when he releases the Oceans and washes away Old Lorule, wishing on the Triforce for a bright future for his descendants.

Ravio, in this, has the Triforce of Prudence, while Kutora/Hilda has Will. (The Lorule Triforce consists of Will, Cunning, and Prudence.)

The title of the game would be Legends of Lorule: Oceans of Change. (Or something like that. Maybe Legend of Hilda: Oceans of Change? I don't know.)

(Also, in Lorule!Child Timeline, that Ravio ends up falling into Holundrum and helping out there, before returning home. He gets off much easier than Hyrule's Hero of Time. that's for sure...)

I have way more Lorule Headcanons than just this... I just thought that these were enough.

...Your headcanon is so good and makes so much sense, I now need to go and rethink my plans for the sequel to Secret of the Great Sea. (I was planning on having the World of the Ocean King being Lorule, but much nicer since the Triforce was never destroyed. Spoilers for an unwritten story.)
For the uninitiated, I'm writing a fanfic series which is basically the Adult Timeline WITH POKÉMON!

Back on-topic, how about the rabbit who saves the Twilight Realm?

Does anyone else think that Termina is Lorule before it became Lorule? What I mean is that it may have been just known as Termina during the events of Majora's Mask and eventually became what we know as Lorule. Link does fall through an immensely deep pit, and all those symbols that flew past him remind me of the light effects that pop up whenever you switch worlds in LBW. Timeline-wise, this may be where Lorule's story began.

...Umm... the effect in ALBW was rainbow distortion, while in MM it was a bunch of icons.