It is probably bacterial blight of lilac.
Management.
https://extension.umn.edu/plant-diseases/leaf-spot-diseases-trees-and-shrubs#bacterial-leaf-spots-1156513
https://www.canr.msu.edu/news/bacterial_blight_of_lilac

https://yardandgarden.extension.iastate.edu/encyclopedia/lilac-bacterial-blight

https://hort.extension.wisc.edu/articles/bacterial-blight/

https://extension.psu.edu/lilac-diseases

http://plantclinic.cornell.edu/factsheets/lilacbacterialblight.pdf

https://www.rhs.org.uk/disease/lilac-blight

That is a difficult question because I am not sure one can even take off all the dead leaves. If the job is overwhelming clean up all the leaves that fall as soon as they fall and mulch under the shrubs after leaf drop to prevent fungal spores being splashed up into the bushes. Prune out obvious cankers.
More information from another expert. 

Thanks for your question and pictures. Your lilac is experiencing a blight condition. This is now extremely common in the Metro area. Some comments:

1). It could be a blight caused by the bacterium Pseudomonas syringae. Among other things, it is characterized by leaf spots that can lead to leaf darkening, leaf wilting, and premature leaf dropping. Fortunately, this is largely a cosmetic condition and unless it occurs over several seasons, there are no adverse effects. It is associated with wet conditions, which certainly describes our current 2024 season. Because this is NOT a fungal pathogen, application of fungicides will do no good. It can be transmitted from one season to the next via leaf debris. To prevent transmission from one season to the next, thorough fall cleanup is essential. See the following for further information and remedial procedures:

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

https://yardandgarden.extension.iastate.edu/encyclopedia/lilac-bacterial-blight - :~:text=Management of lilac bacterial blight&text=Select varieties that have tolerance,bleach solution between each cut.

http://plantclinic.cornell.edu/factsheets/lilacbacterialblight.pdf

https://hort.extension.wisc.edu/articles/bacterial-blight/

https://extension.oregonstate.edu/news/how-recognize-treat-avoid-lilac-bacterial-blight

2). It could be a blight caused by either Cercospora or Septoria fungi. The symptoms are small, brown to black spots appearing on lilac leaves. The distinguishing feature of these spots is that they are surrounded by a yellow halo. Inspect your lilac leaves to see if this halo is present. The leaves will also become distorted and drop prematurely. See:

https://extension.missouri.edu/media/wysiwyg/Extensiondata/Pro/PlantDiagnosticClinic/Docs/leaf-spot-on-lilac.pdf

https://yardandgarden.extension.iastate.edu/article/2021/08/summer-foliar-lilac-diseases

3). It really is not important which type of blight exists; it should not be a fatal situation for your lilacs. Do not feel that they must be dug up immediately and discarded. They will recover although their blooming may be delayed by a season or two. However if you are curious as to which type of blight exists, consider submitting plant samples to a diagnostic disease laboratory for an analysis. This would be a definitive way of getting to the bottom of things. Both Wisconsin and Minnesota have excellent labs to do this. Before submitting anything to either of them, call first as to what type of samples should be submitted. Both have a nominal charge for their analysis. See

https://pdc.umn.edu/

https://pddc.wisc.edu/clinic-overview/

4). There is not much you can presently do to make your lilacs attain a normal appearance. Your efforts must be more proactive, thinking ahead to the 2025 season to prevent a recurrence of this blight. Besides cleaning up and removing all leaf debris at this time (late July 2024), you could cut out a few stems to open things up. Do this cutting just above ground level. The objective is to improve air movement and circulation throughout the bush. This will help in decreasing the spread of the disease.

5). The sites previously mentioned will describe further proactive approaches. In short, they are:

a). Remove and destroy infected plant parts, including fallen leaves and pruned branches, to reduce further spread of the bacteria or fungus. Lilacs are tough; they should withstand this removal.

b). Prune the lilacs to improve air circulation and remove diseased branches. Make cuts well below the visible symptoms and disinfect (solution of one part commercial bleach to nine parts water) pruning tools between cuts.

c). Avoid overhead watering to minimize leaf wetness and reduce the spread of bacteria. Water at the base of the plants.

d). Going into the fall, keep your lilacs well-watered and be sure to do a thorough cleanup of all plant debris.

Good Luck. Please get back to me if you have further related questions. Thanks for consulting us