It's not Bharatnatyam, it's Kuchipudi. As well as I know in classical dance a dancer cannot allowed to lipsync the song , they allowed to express the lyrics by their eyes .
Dear @milisaha847, what I have showcased here is Kuchipudi (Vempati master gaaru's style) only. In Kuchipudi, you are allowed to lipsync the songs as well, apart from the bhava (expression). In Bharatnatyam, yes, dancers do not lipsync. I've been learning this art form for almost 2 decades. This is an old video of mine.