How close are the lilacs planted near the willow tree? And how old is the willow tree, the more mature a willow tree the further the root system will reach out from the trunk. Generally speaking, any plantings over a willow's tree's expansive root system will probably compete for water and nutrients, possibly to their detriment. Shade-tolerant perennials and hardy ground covers are typically recommended to plant over a willow tree root zone.
For more information on willow trees, please visit the following link: