Currently, we know that Lorule is a separate world from Hyrule, but one that draws a lot of similarities with the later, such as the connection between the Triforce and Dark Triforce as well as Hilda and Zelda. As JC said in another thread, if Hyrule is Earth, then Lorule can be likened to hell.
A defining characteristic of Termina is that it's inhabited by the same people living in Ocarina of Time's Hyrule strengthening the connection that it exists in its own parallel dimension because how can someone be in two places at once. Yes, character models were reused due to the N64's hardware constraints and most NPCs were given new names, but even Termina's geography is a distorted reflection of its Hyrulean counterpart.
This apparent aesthetic similarity is strengthened by timeline placement as you mentioned. Links visits Termina on the Child Timeline where Ganon is successfully defeated, therefore there is nothing unusual about the land and its people before the Skull Kid's arrival. A Link Between Worlds, on the other hand, occurs on the Downfall Timeline where Ganon crushed Link and maintained his rule. It would make sense that Lorule is in ruins because of Ganon, potentially being the reason he was sealed away.
I also recognize the counterargument. Ganon and Zelda are completely absent from Termina. They're never seen or mentioned. Ganon is dead so he obviously doesn't make an appearance in MM, but why doesn't Zelda have a Terminian counterpart? While it's unconfirmed what role they play in Lorule, it's been heavily hinted that this world will have a large interaction with Hyrule like the connection between ALTTP's Light and Dark Worlds.
In addition, although there are monarchs in Termina such as the Deku King and Igos du Ikana, there is no Hylian or human like counterpart. In Lorule, it seems Hilda is the leading authority like Hyrule's Zelda. Termina is a dimension gap, whereas Lorule is likely created by the corrupting influence of a dark being like the Dark World in A Link to the Past. There's some characteristic overlap, but Termina is its own dimension (?), whereas Lorule is a mutation of Hyrule.