If your shoots are turning black after the small spots on the leaves appear and enlarge and the leaves hang on and there is what appears to be a shepherds crook appearance at the end of the affected branches, your lilacs may have a bacterial disease called lilac bacterial blight. It is common on most lilacs and especially affects white flowering lilacs but also the purple blooming ones.  According to several extension sites: Lilac blight is difficult to control. The only treatment is to remove infected branches. If your lilac bush does have infection, prune and burn all infected parts as soon as you notice them. This pruning should be done during dry weather when the leaves and shoots are not wet. The hand pruners should be sprayed with Lysol Disinfectant, or a bleach solution (note bleach is corrosive) to avoid spreading the disease (or prune during the winter when infection is low).
It also helps to space and prune your lilac plants so they are not rubbing against each other and air can circulate freely between the plants. Do not fertilize late in the growing season. Clean up the areas below your lilacs and destroy the debris in the fall. 
The disease can also be managed with a spray of a copper containing fungicide applied in the spring just before bud break. While the disease is caused by a bacterium, not a fungus, this fungicide treatment seems to reduce the problem. Generally, infected lilac survives the disease with pruning and perhaps a year or two of copper fungicide treatments  (J. Ball, 8/12/20).