Fushichou no Yume (不死鳥の夢)/theories

Situation Between Cap Boy and Ms. Lemoto
Judging by dialogues before the battle with Mori-san, Bill and Ms. Lemoto. Those three are poachers and since Cap Boy actually is a humanized phoenix, and in some sense a rare kind of animal, Ms. Lemoto decides to catch and sell him to museum for a big money of course. But it could be unfair two on one and plus Cap Boy was very strong so Lemoto gets help from the former poacher Kit-kun.

About the Three Light Pillars
(Spoilers ahead) If the 000000DEM ending as well as the unlocked text logs in the dream world after entering the password in CB's computer were to be considered canon, then all the events of the game are part of a massive VR simulation CB has been trapped in by 000000DEM themself.

Another interesting implication comes from one of the diaries unlocked after entering the password, with it mentioning that the previous leader of the TLP cult wanted to create inmortal people, as he considered humans were limited by time, and with CB being a phoenix-like human, it could make sense to see him as a creation of the TLP. Why was he trapped inside a simulation is unknown, but considering that another diary entry that reveals that 000000DEM killed the former leader of the TLP before them assuming that position, and a text log in the endgame area for the 000000DEM End describing Frost Boy, the NPC that triggers that ending, as "a failure" (and how he couldn't be killed, having been created using a phoenix, so they had to find another way to get rid of him) it's impled that they didn't think very highly of CB or the idea of creating immortal people.

Whether Cap Boy and Frost Boy are the same person or different entities is unknown, as FB doesn't get too much screentime, but the game seems to imply thy are different people.