迷宮入り literally means "entering a labyrinth," and is commonly used for a case or mystery that remains unsolved. In the song, the singer describes the identity of the ever-changing person he once knew as a 迷宮入りの難解なミステリー, or an incredibly difficult mystery he cannot solve.
"CHAMELEON" is a song about running into someone you used to know and realising they have turned into a person you can't read anymore. King Gnu sets it up like a detective story: the singer wants to 突き止めたい (pin it down) but admits 君の正体は 迷宮入りの 難解なミステリー (who you really are is a hard mystery that's gone unsolved). The chameleon in the title is that person, changing colour with every change of heart: 心変わり色変わり (a change of heart, a change of colour).
The verses get very specific. An express train rushes past an empty station platform with a draft blowing through, and she is nowhere to be seen. Later she shows up on a video call screen, already 僕の知らない君 (a you I don't know), laughing so happily that he can't help laughing too. Then the song turns to painting: he keeps covering sad, dirty colours with white paint, again and again (何度でも, "as many times as it takes"), and decides any colour is fine as long as it suits who she is now. My favourite line is the honest one near the end, where he says that putting his feelings into words would just be 単純な強がり (simple bravado). It is a breakup song with no shouting, only a guy squinting at a picture that keeps repainting itself.
Learner tip: watch the two spellings of kanawanai. 叶わない means "it won't come true", while 敵わない in the last chorus means "I'm no match for it". Same sound, different kanji, different meaning.