"Carlily" is the informal, non-canon, out-of-character-only portmanteau nickname of the prospective 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). Currently, the canon timeline has strongly hinted (especially during the Legends of Lavanya Christmas Special) on several occasions that the non-canon idea will become canon reality in the near future.
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. 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.