I asked my Mom for seeds from her lilac bush. Instead of waiting till the fall or late summer, she cut some flowers and brought to my house, sure that they'd produce seeds. My first thought was, 'what came first, the chicken or the egg? These flowers are not going to produce seeds.' I've never been into gardening but as lilacs remind me of my Granny, I want some. Am I just wasting my time saving a dying plat for nothing?
You'll get seeds from the flower buds but only after the flowers have died. Oftentimes the plants from the seeds don't grow into the same type of lilac as the parent bush if the parent is a hybrid. You could try growing a lilac from cuttings, too, but Lilac cuttings are one of the trickiest types of cuttings to keep alive, and there's a very specific way that it has to be done.
Here are some articles that may help you, no matter which way you want to go with growing a new lilac: