Negitoro

LuMiku is the femslash ship between Megurine Luka and Hatsune Miku from the Vocaloid fandom.

Canon
Miku and Luka are both characters from Vocaloid, a voice synthesizing software. They don't have much canon information (like backstory, personality etc.) because they are supposed to be blank slates for the people to portray. Many produce songs with Miku and Luka as friends or lovers.

Songs
Luka and Miku have many songs with them together in a romantic way, that have become quite popular and well known in the community. One of the most famous songs using them is "Magnet" by Minato. Magnet is about how their love is considered “forbidden” because of the homosexual nature of it, but Miku and Luka defies these rules for their love. In the Project Diva MV you can see them in a similar pose to the original art for Magnet. There are plenty of other song including them in a romantic way, some of these songs include:
 * "Kissing Fish" by OSTER Project
 * "Deja Vu" by VocaCircus
 * "Let's Be Honest" by Project OverDose
 * "Suki Kiria" Luka & Miku cover by Hyurno (originally by HoneyWorks)
 * "Acute" by Kurousa-P
 * "Jump For Joy" by EasyPop

Project Diva songs
Project Diva has included a handful of songs into their games using Luka & Miku. One of the most popular using them (Other then Magnet) is "Akatsuki Arrival" by Last Note. In the song, they start out as rivals, but grow to love each other. However, by the time they harbor these feelings, Miku passes away. At the end Project Diva MV you can see Luka looking off into the distant sunset, mourning for Miku.

What does Crypton think?
Cyrpton doesn't really speak on shipping and the like. The only ship they have talked about was the RinKu ship, saying it was the most likely ship they enjoyed. Vocaloid ships will not be canon because as Vocaloids themselves are to be left as blank canvases to content creators and producers.

Fanon
LuMiku is one of the most popular ships in the Vocaloid fandom. It started because fans loved how their voices blended and worked well together. Fans also started making fan music videos and fanart for the two. The LuMiku ship is rivaled by RinLen, RinKu, MikuKAITO, and a few other ships.

Fandom
FAN FICTION