We have seen numerous Lilac samples this season with similar symptoms; leaf damage this time of year is often tied back to infections that took place in spring and remained fairly asymptomatic until summer conditions stressed the plants. Lilacs can be vulnerable to powdery mildew and bacterial leaf infections which can cause damage to the leaves that results in necrosis (portions of the leaf dying) and premature leaf drop. The multiple late-spring frosts we experienced this season also could have damaged tender foliage, making them more vulnerable to infection.
No treatments are needed (or even effective) this late in the season. Next year, infection severity will partly depend on the weather, but if needed, a copper-based fungicide can be used to help prevent infection. Fungicides are not curative and will not impact infections that have already taken place so they need to be applied early-on, when leaves are still young. Treatments will also need to be repeated, though at what interval depends on the product.
The more important action to take will be to remove all of the Lilac's old wood, as this not only loses vigor and blooms more poorly as it ages, but also becomes more of a target for larvae of wood borers. It is normal and beneficial for Lilacs to sucker (produce basal sprouts like in the picture), but some of the excess need to be thinned-out so they are not so crowded, as crowding promotes conditions conducive to disease spread. These young stems replace the old ones that are removed, producing growth that will flower well and be more vigorous overall. Cut down stems with a folding pruning saw as it's easiest to squeeze into tight spaces and cut as low as you can go without damaging too many other stems in the process. All of the old stems can either be removed at once (around February or March) or gradually by taking a few out each year until all are gone. Flowering may temporarily decrease as the new growth matures and reaches flowering age. There isn't a hard-and-fast guideline as to how thick of a stem to remove, but start with the thickest; you can always see how they perform in spring and remove more in future years.
Make sure plants are still receiving full sun (six or more hours daily in summer), otherwise the pruning and disease prevention will have limited benefit; Lilacs loose vigor if sited in too much shade. If they are more shaded than they used to be, see if you can relocate them by digging up the root balls and re-planting. Early fall is a good time for this, but otherwise spring will suffice as well.
The emptying of the downspout into this bed is not ideal, as it delivers a lot of excess water during rainstorms. Waterlogged soils, even if temporary, deprive roots of oxygen which can either kill them outright or stress them enough to allow opportunistic pathogens to infect them; these infections are not treatable once set-in. It would be best to continue directing the roof drainage further from the house and garden by adding (buried) pipe and positioning the outlet either into a rain garden or into an area of the yard that drains very well. Lilacs do not thrive in overly-wet soils.
Wow--thank you so much. That was extremely helpful.