This information is late so treat it as a f.y.i.... I usually prefer to send samples of affected leaves to someone who can diagnose the problem because applying a fungicide will only work if you apply the fungicide that affects the causal agent. For example,
* some brown dots are usually caused by fungal agents for which there is not treatment so the best one can do is dispose of the affected leaves in the trash, water the plants early in the morning by watering the soil, not the leaves, control soil moisture if the soil is very wet. If not controlled, the brown dots enlarge into brownish or yellowish areas that can cover the whole leaves.
* a bacterial infection commonly attacks white flowering lilacs via lesions in the tree, leaves, etc. the dots start yellow or brown and then turn black eventually causing the leaves (and blooms sometimes) to wilt. Improved air flow and more sun seems to help. Soil defficient in minerals or soil with very high nitrogen levels weakens the plant so make a soil test and take appropriate action. Some people will remove (prune) the affected area by cutting about a foot below it. Being a bacterial infection, I suggest you use alcohol on the pruners after pruning. Water the soil as mentioned above.