Sounds like mildew, a fungus. Cure is more light and air, especially light. Half to more than half shade is not enough sun for lilacs. They need full sun.

If you have lilacs, you need to do your research on powdery mildew, probably THE most common disease of these plants. It can be very troubling for your lilac if steps aren't taken, all year along, to prevent and manage this disease.

Mehitabel is absolutely correct in reminding you that lilacs require full sun conditions. That means at least 6 full hours of direct sunlight, if not more. The plant should also be sited in a location that gets good air flow. You can improve both sunlight penetration AND air circulation by thoughtful and careful pruning to open the plant up. Wait until winter to do this so that you can see the bones of the plant better.

Powdery mildew is one of the few fungal disorders that is not triggered, spread, or exacerbated by water. As a matter of fact, if caught early on, rinsing the plant off with plain water can prevent true infection. Do this daily as soon as you spot the hint of PM on your plant.

It's been shown that timely neem oil applications can both prevent AND cure PM infections and I recommend that you try it. An application of horticultural oil can be highly effective, too. Spray the plant in the dormant season as well as during the growing season.

PM will overwinter in the leaf buds of a dormant plant, so beware. Oils can help with that.

This fall, after all of the leaves have fallen, do a good clean up of the area. Remove any mulch that you may have used along with the fallen (and infected leaves).

There are assorted chemical fungicides for PM, too, but you can pretty much prevent a major outbreak if you follow the above cultural chores and try the water, neem, and/or oil.

I suggest that you do some reading on PM control, PM and water, PM and pruning, lilacs and PM control, etc. Google is your friend.

Oh, I should mention that you'll probably (hopefully someone will mention it) read that a late season infestation of powdery mildew does not constitute a crisis. Your lilac is entering the slow down to dormancy and those leaves are getting ready to say 'bye-bye' pretty soon, anyway.