Lion Lilies are grown in the Haighlei Empire and are reserved for the monarchs. They are described as "huge, tawny-gold, many-petaled bells on long, slender stems" with a "heavy fragrance." [The White Gryphon, chapter four]
When an emperor wishes to pursue a romantic relationship, he expresses it with the Lilies. Sending three Lilies is an expression of interest. Four is more than just interest. The next step is sending a bethrothal-necklace, which acts as a marriage proposal. It is up to the lady to accept or decline the gifts, thus giving the emperor an answer to his question.
Emperor Shalaman sent them to Winterhart when she visited his court as part of the treaty negotiations between Kmbata and White Gryphon. He got as far as four Lilies before Silver Veil explained their meaning to her. Winterhart and Amberdrake then explained about their lifebonded status as a means to refuse his further advances.