Makers of Fine Wands Since 2007
Lily Potter's Wand

What we know of Lily Potter's wand comes from Ollivander's first conversation with Harry when Harry buys his first wand.  Ollivander describes it as willow, 10 1/2 inches, flexible, and good for working charms.  He does not mention the core.  Based on that, what little we can say about it is this, which seems to suit Lily rather well:

Willow with unknown core, 10 ¼ inches

Willow is a pioneering wood, first to take root, stabilizing its environment.  Sacred to Hecate, Circe, Hera and Persephone, it is the Tree of Enchantment and is associated with the moon.  It protects against harm and evil intent, and heals.  A very feminine wood, Willow is associated with the cycle of life, promoting love, growth, and fertility.  Because of its stabilizing influence, Willow banishes depression and sorrow and can help the user overcome loss.  Although it strengthens the user’s psychic energy, Willow can be indecisive, so it is best partnered with a person with strong sense of direction and a strong will.  It is a very good wand wood for a strong, unconflicted individual.  Willow is particularly useful in divination and the granting of wishes.  Its elements are Earth and Spirit.  Calendar dates for Willow: April 15 – May 12.  In Common With: Ron Weasley