Lumither

"Yes, of course. "Home" is wherever we are together."

- Archon Quest: Chapter 1 - Act 4: We Will be Reunited

Lumither is the family ship between Aether and Lumine from the Genshin Impact fandom.

Canon
As Aether and Lumine finished venturing out of Teyvat 500 years ago, before all the characters we now see existed, and so they find the "Seal of Teyvat" which sealed Teyvat from other Continents (as it is just a Continent and there may be other Continents surrounding it), they get stopped on their way by one of The Heavenly Principles of Celestia.

The Unknown Goddess attacked the siblings and captured the both of them, sending nightmares on their seal. Those nightmares would be probably the thing they will do when they are separated, and one of them gets sent down to the starting point (or Starfell Valley) and dragged to the Abyss Order by some Abyss Members.

Meanwhile, the other sibling wakes up and gets their power sealed away, trying to find a way to discover their lost sibling.

The remaining of the story is left to whether or not the Traveler progresses through the story, and the longer of the story that doesn't progress is left behind, the Abyss Order will become more powerful.

Archon Quests
In the Prologue of the game "The Outlander Who Caught the Wind", The Knights of Favionus asked the Traveler what reward they wanted for defeating Dvalin and saving Mondstadt, to which the Traveler replied that they wanted Missing Person Posters put up around Mondstadt to look for their lost kin.

Later, Chapter I of the game "Farewell, Archaic Lord", the Traveler repeated this sentiment, requesting for Missing Person Posters be put up around Liyue Harbor. During the Lantern Rite Festival Event, the Traveler made a wish for their respective sibling, stating it's their sibling's deepest desire or the Traveler hopes that their sibling's wish will come true.

Bough Keeper: Dainsleif
In act I, the Traveler met Dainsleif after fighting the enemies, the Traveler sensed something familiar at a cliff, they then went to the cliff and examined the Dandelion, there was a rewind that was from the beginning of the game, if you picked Aether as the MC, he then says "This dandelion...reminds me of..." or "I...could feel her." And if you then picked Lumine as the MC, she then says "This dandelion...reminds me of..." or "I...could feel him.", after that the Traveler then had to get to the bottom of this but Dainsleif stopped the Traveler, Dainsleif was also now leaving.

In act II, at the end of the act. After the Traveler tries to defeat the Abyss Herald, The Abyss Herald creates a portal but Dainsleif stops the Abyss Herald and the Traveler's sibling appears. The Traveler was happy to meet them again although Paimon notices that the Traveler's sibling blocked an attack against the Abyss Herald. The Traveler's sibling continues to tell the Traveler to not team with Dainsleif because he is their enemy. The Traveler's sibling now says to not stop in the abyss. The Traveler tries to tell their sibling to come home with them, although the Traveler's sibling refuses. The Traveler was confused, the Traveler's sibling tells the Traveler that they have already traveled through this world (Teyvat) once. Once they reach the end of their journey as they did, they will see for theirselves the true nature of this world. (Teyvat) The Abyss Herald now created another portal meaning that the Traveler's sibling would now go but the Traveler tried to get them but the Traveler didn't get to the portal in time while Dainsleif was gone because he went in through the portal. Paimon tells the Traveler that show them (Traveler's sibling) what they're made of.

Story Teaser - We Will Be Reunited
In the story teaser, we see Lumine's perspective. She acts as the antagonist and we see what had happened to her in the time that she was away from her brother. In the middle of the video, we see a Hydro Abyss Mage appear and report to her. The Hydro Abyss Mage tells her that someone interfered with the plan to make Stormterror into a weapon and Lumine assumes it is due to the Ameno Archon and questions if he rose again to free the dragon, but the Hydro Mage tells her that instead, it is her brother that is the "issue". When Lumine hears this, she has a flashback from a time when she and her brother were separated by the unknown god. Lumine then instinctively runs to a cliff in Stormterror's Lair, from where she sees Aether fighting against Hilichurls with Paimon. She then says: "We will be reunited, dear brother. But not here. Not now." She says that they will meet at this journey's end, once the dust has settled. When Aether finishes fighting, he goes away with Paimon, after which we see Lumine sitting inside the hand of a Ruin guard and the Ruin guard taking her away into the sunset, and so the teaser ends.

Quote
"May you find your kin at the end of that journey. Well then, let us part ways here for now."

- Dainsleif to Aether/Lumine

"We will meet at this journey's end... Once the dust has settled."

- Lumine to Aether

Fanon
This ship is rather popular as a familyship, due both of them being canonical siblings. Although, they haven't had much interaction in the main story, it's clear that the Traveler cares about their other sibling and wants to get their sibling back at any price. This ship is quite popular as finding the other sibling is one of the biggest themes in the story.

Due to both of them having a clear sibling bond, this ship isn't popular as a het ship, as incest ships aren't exactly popular in the fandom. However, there are still a minority who ships them as a het ship. It is rumored that miHoYo loves to make their games sad and have a sad ending, and as such there are a lot of theories that the twin that the player did not choose would die or betray the twin chosen by the player.

This ship currently has 1300+ fanfictions on AO3, with the majority featuring them being shipped as a family.

Fandom
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Trivia

 * In the voiceline "About Being Siblings", it's confirmed that Lumine and Aether are the exact same age, and that they decide who has to do errands with rock-paper-scissors.
 * According to the Chinese, Japanese and Korean pronouns the twins use to address each other in the opening cutscene and in later interactions, Aether is the older twin and Lumine is the younger. With the English translations not making any distinction on which is the older/younger twin.