I'm not quite convinced this is a 'lie detector'. I think this is a representation of how easily - or not - each character says "sorry".
Not to overexplain anything, but from this I get that Utena is a chastened, but she stills apologizes. And, of course, she'll apologize for her wife and child. Kiwi is... 'reluctant'. Arisu is, presumably, mute. Matama starts and stops, and it's hard, but she can say sorry. Haruka and Sayo are good girls so they immediately apologize. Karouko will apologize, backhandedly probably, or in an insulting way; "Sorry you're so dumb", maybe?
And so on. That's how I interperted it, anyway. I think it really captures their characters with just a line, and I think that is really cool.