No, I'm not comparing both CAROLS I've posted and saying she lip-synched for one. I'm just saying that I wonder how she can pull her mic so far away from her mouth, adn yet there's no difference in her volume/strength.
Maybe it'll help if I say it this way. Like the last phrase of the part is "nai kedo". The mic is right beside her mouth when she sings "nai", she pulls it far away at the word "ke", and it's right next to her mouth again on "do". But if you don't watch her do this, and just listen to the audio, the whole phrase "nai kedo"flows without change in volume. Though when you watch the video you would expect her voice to thin a little on "ke" since you see her pull the mic away. The 2 performances I've uploaded are those that I see her doing the pulling-mic-away thing.
Hope that helped

I'm not trying to prov that ayu's lip-synching, but just bringing it up cause it struck me as weird..