Certified GKH Gardening Expert
Your photo did not come through. I will only be able to take a few guesses at what is going on.
This could be overwatering, fungal infection/bacterial blight, or could be deficiencies. Without seeing the exact placement of the damage, it would be very difficult to give you an answer.
You can have your soil tested by your local extension service, which you can find here: https://www.gardeningknowhow.com/extension-search
This article will help you to know what is the correct care for the plant: https://www.gardeningknowhow.com/ornamental/shrubs/lilac/lilac-care-growing-and-planting-lilac-bush-plants.htm