This theory has bugged me for awhile. For years I've seen it pop up every once inawhile but nobody has ever fleshed it on most forums I join. So my goal is to revise it for the forum to finally get some full on debate going about this theory. It's a work in progress.
Note: This theorizing will be done from an in-universe point of view, meaning that I'm looking at this theory as if Hyrule and Lorule are real. This is extremely important, as doing it any other way would open up the argument that games that were created before A Link Between Worlds would not be able to reference Lorule because it was not created yet.
Before I begin I'm going to admit that I don't know if I'm personally going to adopt this theory yet. The thing I hate about it is the fact that with all the evidence gathered it all seems to imply that Demise is from Lorule. We just can't take it any futher than that implication which bothers me. To start, I think it's important that we know who Demise is before we even jump into the the theory.
Who is Demise?
Fi in Skyward Sword says this about Demise:
"This eternal being has conquered time itself. It is the source of all monsters." - Fi
He is basically the embodiment of all evil, supposedly. His main role in the series was to serve as the source for the re-occurences of Ganondorf by setting his hate curse upon Link and Zelda.
“My hate... never perishes. It is born anew in a cycle with no end! I will rise again. Those like you... Those who share the blood of the goddess and the spirit of the hero... They are eternally bound to this curse. An incarnation of my hatred shall ever follow your kind, dooming them to wander a blood-soaked sea of darkness for all time!" - Demise
Demise's sole purpose is to obtain the Triforce and destroy the gods at all costs. That's pretty much it. Because he had such a short appearence and the game didn't go in depth on his backstory (telling us were he came from, why he just hates the gods for no real specified reasons, etc...), it left the door open for theories like this one.
Lorule, a parallel world and it's counterparts
Lorule is very similar to Hyrule. While Termina is stated to also be a parallel world to Hyrule, Lorule resembles Hyrule more than Termina does (in ways). Notably, Lorule has a Sacred Realm, a Royal Family, and clear counterparts to Link, Zelda, and Ganondorf (Ravio, Hilda, and Yugu). Futhermore it had a Triforce of it's own which is very interesting. Though the game states the Triforce in Lorule was depended on too much. When war broke out over it Hilda's ancestors destroyed it in hopes of returning peace to the land. Instead Lorule fell futher into turmoil and is close to crumbling during the timeframe of A Link Between Worlds.
We have a consistent equivalent to almost everything in Hyrule, what we are missing is a Master Sword.
Demise might orginate from Lorule?
For the sake of easy transition I'll begin to tie key points together starting with the Lorulian Master Sword. In A Link Between Worlds there is no Lorulian equivalent to Hyrule's Master Sword. The whole reason Ravio seeks Link's help is because he has no Master Sword of his own to use in Lorule. The question that arises is why isn't there a Lorulian equivalent to it? The answer is that there might be a Lorulian Master Sword and Demise weilds it. At the end of Skyward Sword it is revealed that Ghirahim was actually a being that resides in a sword, like Fi. Demise reverts Ghirahim into the sword which he really is. The sword has often been speculated to be the anti-thesis to the Master Sword. Possibly the Lorulian Master Sword, designed for a different purpose than to fight evil obviously? It has the inverted Triforce on it. It's a backless assumption because we just don't know, although it explains why Lorule is missing a Master Sword equivalent — Demise took it to Hyrule and was killed.
This next point is also very interesting. Demise and his army came from a fissure.
"One dark, fateful day, the earth cracked wide and malevolent forces rushed forth from the fissure. They mounted a brutal assault upon the surface people, driving the land into deep despair... They burnt forests to ash, choked the land's sweet springs, and murdered without hesitation. They did all this in their lust to take the ultimate power protected by Her Grace, the goddess." - Introduction (Skyward Sword)
In A Link Between Worlds fissures serve as portals linking Hyrule and Lorule. The fissures are created due to Yugu's actions, but what we know is that there was a ancient crack linking Hyrule and Lorule together on a stone slab inside Lorule's Sacred Realm which Yugu discovered.
"Yuga discovered that there was a strange crack in this grim slate... Through it, we could sense that there was another world beyond ours... a place where the Triforce still existed." - Hilda
This could have been were Demise learned of Hyrule as well, assuming he is Lorulian.
His motive for going to Hyrule would be to obtain it's Triforce. Denied the Lorulian Triforce it makes sense for him to take his army to Hyrule using a fissure serving as a portal between the worlds. Maybe it was his army that marched an assault for Lorule's Triforce also? I do think that the difference in what timeframes both worlds are in matches. I'm under the impression that when Demise came to Hyrule Lorule probably would be about mid-way through it's history (having Triforce issues and all that). Hyrule would be at an early point in it's history so it'd make sense for Demise to end up in the timeframe he did. We also see that mid-way into Hyrule's history Lorule is on the verge of the end of it's own. If things would have continued on like they were Lorule would have fell to ruin.
To conclude, we must ask ourselves were these similarities intentional, or coincidental? After writing this I feel like there is so much mystery still shrouding the theory that the evidence gathered can niether prove or disprove it's validity. What we need is a smoking gun proving a connection to Demise and Lorule, unfortunately there isn't one. If we could just get more info about Demise, even the sword itself that could be enough to put this theory to rest.
I do know that there are conflicting theories on certain aspects of this theory which is why I encourage people to come forth with those theories. I think this has potential to spark some great discussion. So feel free to share other theories. Maybe you have a different idea about Demise's orgins? Maybe you have a theory about why Demise's Sword can't be from Lorule (I know such theories exist). I'll be looking foward to seeing were this goes.