Lilac bushes bloom only once each year, in spring, but they make new buds after they bloom. The buds become the next year’s flowers. If you trim a lilac bush too late in the year, then you’ll cut off unwanted branches and next year’s blossoms.ethod. As soon as the lilac bush's flowers are dead, trim each flower stem back to the leaves, removing all trace of the flowers. This step stops the lilac from using its energy to make seeds.