How does Persse McGarrigle meet Lily Pabst?

Persse McGarrigle finds Angelica, finally, in an elevator, wearing a red silk dress, and without speaking, pulls her to him and kisses her deeply. Then, when he declares his love of and desire for her, she leads him to her room, where they make love for hours. Finally, spent, he says she will have to marry him and she tells him that, in fact, she is Lily, not Angelica.