This could be a fungal disease known as Lilac Pseudocercospora Leaf Spot, but to be sure, a sample should be sent to the Plant and Pest Diagnostic lab on campus: https://www.canr.msu.edu/pestid/.

Fungicides should not be applied at this time.  Fungicides are preventative, not curative.  They should only be applied if it has been confirmed a fungus is present.  

It is also possible that the lilac needs to be pruned.  If you haven't pruned it in several years, it may need a renewal pruning.  This will allow the younger growth to develop and opens up the lilac for better air circulation.  This should be done in late winter or early spring.  You will sacrifice the blooms that year, but for the overall health of the lilac, it's worth it.  This article from the University of Maryland extension explains the different types of pruning: https://extension.umd.edu/resource/pruning-shrubs-and-hedges-home-garden/#:~:text=Renewal%20pruning,the%20empty%20spaces.

Thank you for your question.