紙一重 literally means "one sheet of paper," expressing an extremely narrow difference or boundary between two things. In the song, it describes pleasure and danger moving across a razor-thin line, making this poetic idiom especially memorable and emotionally charged.
"Vanity" by Janne Da Arc is a song about loving someone who belongs to somebody else, sung by the person stuck in the middle. The narrator knows this woman through nights together, and he admits that in bed he gets "少しだけ意地悪になる" [a little bit mean]. He also tells us straight out why he never asks about the rest of her life: he is "現実 から逃げているだけ" [just running away from reality], because he can already see how it ends. His wish is simple and a bit desperate: "朝が来なければいいのに" [I wish the morning would never come].
The detail that sticks is the ring. "左くすり指に" [on her left ring finger] sits "光る目ざわりな指輪" [a shining, eyesore of a ring], and because of it "Kissが苦い" [the kiss tastes bitter]. くすり指 literally means "medicine finger", the everyday Japanese word for the ring finger, so the line is clearly pointing at a wedding or engagement ring. Then he asks the question he hates asking: "今夜は彼の腕の中で夢を見るの?" [Will you dream in his arms tonight?]. He even wonders if she is just tired of "火遊び" [playing with fire], the Japanese idiom for a risky affair. My favourite moment is the last line, which is quietly brutal: "触れあう度に 君が遠くへ見える" [every time we touch, you look further away].