Fushichou no Yume (不死鳥の夢)/theories

Situation Between Cap Boy and Ms. Lemoto
Judging by dialogues before battle with Mori-san, Bill and Ms. Lemoto those three is poachers and since Cap Boy actually is humanized phoenix and in some sense a rare kind or even animal Ms. Lemoto decides catch and sell him to museum for a big moneys of course, but it could be unfair two on one and plus very strong Iemoto and Cap Boy get help from 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 him(?)self.

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 phoenixlike 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 him(?) 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 he(?) didn't think very highly of CB or the idea of creating inmortal 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.