But she fully is Italian.
Her surname is composed of both the surnames of her paternal grandparents, Nobile Ettore Bernardo Rosboch and Baroness Elisabeth Jaworski von Wolkenstein (who herself used the surnames of her parents, Baron Romuald von Jaworski and Countess Maria von Wolkenstein).
However, it is known that her biologic paternal grandparent isn't Ettore Bernardo Rosboch but Don Filippo Caracciolo, Prince of Castagneto and Duke of Melito.
In terms of ancestry and blood,both her father Ettore and her mother Anna Maria (Lilia) have descended from various Italian,German,Austrian and even Polish(Jaworski) noble families...
As to her predicate nobile...the Rosboch family was bestowed the nobility on Italian Senator Ettore Bernardo Rosboch and that's why Lili and her father officially have this predicate nobile...while von Wolkenstein part of the family name came through Ettore's mother Baroness Elisabeth von Jaworski,whose mother was Countess Anna von Wolkenstein-Trotsburg und Neuhaus...