White powdery coating on lilac branches that rubbed off on a dog is unlikely powdery mildew (which doesn't transfer in clumps). This suggests cottony scale (Pulvinaria spp.)—insects producing white waxy egg sacs that easily dislodge.
Pick at the white material:
If powdery mildew: Usually cosmetic on lilacs; ignore or spray sulfur/fungicide at first sign next spring.
If cottony scale: Apply imidacloprid soil drench (systemic) or horticultural oil at crawler emergence (late spring). Prune heavily infested branches.
Powdery mildew is annual and harmless; cottony scale weakens the plant and spreads. The dog test is a reliable differentiator.
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