This song is set to be released on the OSSCE album in a few days. Since it's set between Moonlit Bear and Survival MA on the tracklist, it seems like the song takes place between Meta's death and Elluka and Irina's selection for the seventh project.
This song is about the fifth Project MA, where only one child was born. Her mother was "punished" for her failure to birth twins, and so she didn't raise the child she gave birth to. Given the purpose of Project MA and the two successful pairs of twins - Hansel and Gretel, and Marina Lucif's stolen babies who would be the ancestors to the Lucifenian line - being Rin and Len characters, this "only child" must either be a Rin or Len character - and this means their counterpart is missing, because they were never born and possibly never conceived.
We have a Rin character from about the same time period who we don't know the identity of - from the very beginning of the timeline.
Barisol's Only Child is the singer of Full Moon Laboratory. She was created, so she has a reason to be present in the experiments to create "the person who created her". Her lack of a Len counterpart is because she was part of the failed project.
Possibly, Irregular is the counterpart she would have had if the fifth project had been a success.