They have powdery mildew. A very common disease of lilacs late in the season. Your plants are *not* dying even though they look really nasty.

If they haven't had this disease in previous years, you've been lucky. Further, the new hydrangeas don't have anything to do with it. Instead, the environmental conditions this year (weather) have apparently been extremely favorable to powdery mildew.

The only thing to do at this time is make certain all the affected leaves are removed after they fall/drop.
Definitely too late for any sort of spray.

Powdery Mildew appears as a white, dusty covering on plants leaves and can be rubbed off somewhat.
Lilacs are quite susceptible to PM, but it can be easily controlled early with either a spray made of 1 teaspoon of Baking Soda in 1 quart of water or a 50/50 mix on fat free milk and water.
The link below provides some very good information about Powdery Mildew, the conditions that cause it to flourish, and how to control it.

Here is a link that might be useful: Powdery Mildew control

its too late to do anything about it.. as jean notes ...

and as kim notes.. you prevent or control it ...

hot muggy nights in july and august is the perfect time for it to explode ... so prevention starts in june or so ...

in 35 years of gardening .. i have never treated a lilac for such.. frankly its endemic to the plant... and not worth my time, effort or money to deal with it ...

and it will NEVER kill a lilac ... almost nothing will ...

ken

Thank you all for your answers. The reason I ask if the lilac is dying its because of the bushes already dried up. This was the first one to get this powdery mildew. See the attached picture.

That plant died from something else. They also get a bacterial canker which can kill, possibly other things.