Lumine first meets Eula, after fighting the Fatui. A Fatui Agent nearly kills her from shooting her a far, but the shot is blocked by Eula who arrived to the scene on time. She kills the Fatui Agent. After that, Eula asks her if she knows how long that she has been tracking these targets, and now she tells her that she thinks she's stronger because she got to them first, and then says "vengeance will be mine!". Though Lumine didn't had any idea what she meant by vengeance.
Eula says that she has heard the commotions and came swiftly as she could, only to find her fighting the Fatuis already, and she was making quick work of them too. She says if she didn't make her move, Lumine would've took all the credit. Though Eula was glad that she was unscathed, saying that confronting the number of Fatuis at once can be dangerous. Lumine tells her that she's used to fighting with the Fatui.
Paimon on the other hand, still didn't understand her but thanked her for her concern, but Eula says why would she be concerned for the safety of her arch-enemies, saying that Lumine is her arch-enemy. Though Eula mean by, she would have to escort 2 strangers to Mondstadt that took her target, if they were injured. Which will cause her even more trouble.
Lumine then asks her if she must be Eula, Eula says yes but asks how does she knows her name. Paimon answers with, they were trying to investigate an aristocrat named Schubert Lawrence, Eula understood them and told them that it was his uncle. But asks her why are they trying to investigate him, in which, Lumine answers with, "He may be secretly involved with the Fatui.". Eula chuckles saying, she has some nerves defaming a family member right in front of her.
Though Paimon told her that it was an assignment from Jean, it's just an investigation. Lumine asks her if she's worried/curious about her uncle. Eula answers her, saying that everyone in the Lawrence Clan is a scum so rumors and unwarranted gossip are natural. Eula tells her that they only just met, saying it has been a while since she encountered anyone as interesting as her.
EuLumi is a small ship in the Genshin Impact fandom, and is considered to be a rare pair. It's often overshadowed or rivaled by the other ships such as; ChiLumi, Lumber, and EulAmber, being their most popular ships. EuLumi only has very few fanfictions on Archive of Our Own.