"Carlily" is the portmanteau nickname of the romantic couple of Lily Brightendale and Carmen Calandra. While the portmanteau was born prior, the concept of the yuri relationship was born on a particularly inspiration- and drama-filled night on the Athalia Academy Active Posting Pad (specifically, July 14, 2014).
On the night of February 17, 2016 (at the beginning of Season Four), almost exactly a year and a half after the idea was conceived, Carlily officially became a canon relationship, having been informal and non-canon only up until this point. In the midst of an unusually active and productive night on the Athalia Season Four Etherpad, HylianRose and Driving Park (Carlily's creators) decided to wrap up the (dead) Christmas Special with Carmen and Lily completing their gift exchange with a small gift Lily was saving for Carmen that was introduced early on in the Special. The gift was a ring, and Carlily officially began their relationship then. This interaction was chronicled in Lily's first in-character post in Season Four.
The Carlily relationship idea spawned a fanfiction roleplay that depicts the future life of married Lily and Carmen. It has been steadily progressed for many months, being roleplayed on a dedicated Carlily Etherpad and then archived on the Yuku. As of 2/17/16, when the Carlily relationship became canon, the complete fanfiction also became canon, adding millions of years to the Athalia universe timeline. In addition to the main storyline which takes place about twenty years after the main Athalia Academy seasons, the Carlily fanfiction also has two spinoffs. The first is a five-chapter short story written primarily by Driving Park but with the help of HylianRose for Lily's lines. Called "The Last Skylark", it is set in 4994 A.D. and focuses on Carmen's death. The second is as-yet untitled and takes place millions of years after "The Last Skylark". It focuses on Lily's exploits as Gabriel Foster after she comes down from heaven, and also features chukklehed, who plays an A.I. unit.