Ok but this is actually a really good idea and I hate that they didn't go with that.
There actually is a theory that the reason why Lorule does not have a Master Sword is because it has Master Ore that can only be found in Lorule and not Hyrule.
Master Ore is what is needed to upgrade the Master Sword by taking it to a smithy and using the Ore for the upgrade.
The theory goes that Lorule deviates from Hyrule by lacking a Demon King and a Hero, with Ravio being instead the Lorulean counterpart to Hyrule's Link. While Link is heroic and courageous, Ravio is a bit more freeloading and cowardly.
So as a result, Lorule had no Hero to help defend the Kingdom, and thus Hilda wished for the Lorulean Triforce to be removed from existence so as to no longer tempt the hearts of covetous people to do heinous things; unknowingly condemning Lorule to its darkened fate.
Without an ever-reincarnating Hero in their mirrored version of Hyrule's history, Lorule had no need to forge their own Master Sword. Hence why Master Ore exists in Lorule while it does not exist in its raw form in Hyrule.
Because all the Master Ore of Hyrule was used to forge the Goddess Sword that would become the Master Sword.
And now, because we used the Master Ore to enhance the Master Sword, Lorule is forever without an equivalent to Hyrule's great blade.
So should a Demon King arise in their world - Lorule would be doomed without a Master Sword.
A grim theory.
And yes, I hate that we didn't get a Lorulean equivalent of the Master Sword. I could imagine the blade being designed as an opposite to the Master Swords design.
The Master Sword has the blade start out narrow at the cross-guard, then becomes broader for the Triforce Insignia, and then remains a broad width down the length until we reach the tip.
So to fit with Lorule's thematic mirroring of Hyrule, logically the Lorulean equivalent would be the opposite with a broader start to the blade at the cross-guard, the insignia, and then narrowing after the insignia to be a thinner blade that stays at that width until the tip.