* Λείλα (Leila): While Arabic in origin, it has a similar sound and also connects to night and beauty.
* Κρίνος (Krinos): This means "lily" in Greek, but it's masculine. A feminine variation might be needed.
* Καλλιρόη (Kallirhoe): This name means "beautiful flow" or "beautiful stream" and evokes a sense of grace and beauty.
* Άννα (Anna): While not directly related to lily, Anna has a similar delicate and classic feel.
Ultimately, the "best" translation depends on your interpretation of the name Lillian and the feeling you want to convey. There isn't a perfect single word equivalent.