There’s a MAC red lipstick in the dressing room where Arthur (Joaquin Phoenix) sits while waiting to perform at the Live! With Murray Franklin. I guess he used the same lipstick to write “Put on a happy face” on the mirror.
Seeing this lipstick here is not a surprise, because MAC was the brand of choice of the movie’s make-up artist, Nicki Ledermann, who used Chromacakes to create the protagonist’s clown looks.