Most powdery mildews on shrubs and trees do not have a significant impact on plant health. There are times, however, when management is needed, especially when plants have suffered repeated infections for several years. In many of these cases, cultural practices will control the disease. Plant in areas that are proper for the plant species. Place plants in sunny locations with good air movement. Do not crowd (allow for good air circulation) plants. Dense, shady, or damp areas favor disease development. Remove and destroy dead foliage around the plants in the fall to decrease the level of infection next spring. Maintain healthy plants, but avoid excessive fertilization and watering as these practices encourage succulent new growth, which is more susceptible to powdery mildew. No overhead watering as wet leaves can be magnets for infections. Resistant varieties continue to offer the best source of disease control. If infections occur early in the growing season, fungicides can be used to reduce infection, but treatment must be started as soon as the first symptoms are seen. Once the disease becomes widespread, it cannot be controlled in that year. Chemical control is not recommended for infections that take place late in the growing season. Understand also that fungicides can halt progression but do not cure. This why if you are going to use a fungicide at any point, it has to be done early, as soon as irregularities are seen. Powdery mildew is very common on lilacs.

Your leaf spotting appears to be fungal, usually without detrimental plant affects. Best option so late in the growing season is to do nothing. New leaves will likely come in just fine in the next growing season. Picking up and disposing of fallen leaves this season is recommended as many funguses can overwinter in the soil and reinfect in the next growing season. Getting the correct diagnosis is still recommended however.  You can do that by sending a sample to Diagnostic Services.  They will culture out your sample in the lab offering a positive ID and management recommendations for a small fee. https://pestid.msu.edu/   

Here's more on leaf spot issues:
 http://www.missouribotanicalgarden.org/gardens-gardening/your-garden/help-for-the-home-gardener/advi...

Does not appear to be symptoms of bacterial blight: http://extension.illinois.edu/hortanswers/detailProblem.cfm?PathogenID=52