This purity is not virginity; rather, this purity is knowing what you want and never settling until you get what you desire. You don't alter your desires or ambition despite the circumstances, but keep true to what you truly desire. Instead of allowing the thorns of "personal contact" or attempts at intervention that third parties may have tried to force on her, the Lilly maintains her resolve and stays true to what she knows she desires.
This purity isn't virginity; rather, it's knowing your goals and never giving up until you achieve them. You don't change your ambitions regardless of the situation, but stay true to what you truly desire. Instead of being influenced by third parties' attempts at intervention or "personal contact," she maintains her resolve and stays committed to her desires.