Good Morning, 

Thank you for contacting the U of M Extension Service. 

Please click on the following link from the U of M Extension Yard and Garden website:

https://extension.umn.edu/plant-diseases/leaf-spot-diseases-trees-and-shrubs#bacterial-leaf-spots-and-blight-1156513

Please review the above information. It is a bacterial blight. Scroll down to the bacterial leaf spots and blight section.  That refers to the section on Management.  Your lilacs will probably survive but they may not be pretty this summer. 

Good Luck!