If neighbor plants look healthy, then it is probably not chlorosis caused by iron deficiency or other general problems with the soil.
As I understand your question, it is not a container plant, and then it seems to be safe to rule out overwatering unless the area has been soaking for longer periods.
You also noticed brown spots which could indicate a fungus:
Various fungal diseases potentially attack lilac foliage, often appearing as brown or dark spots or irregular areas that may be accompanied by a yellowing or browning of a lager leaf surface area and sometimes leaf drop. Damage is usually not severe on established, vigorous plants.
Rather than trying to determine exactly what disease that is causing these symptoms, I suggest to focus on cultural controls for treatment like pruning of unhealthy parts and keeping distance to neighbor plants:
- Maintain adequate spacing between plants and prune to provide good air circulation within the canopy.
- Prune out and burn all affected tissues immediately.
- Plant resistant species or cultivars.
- Do not fertilize late in the growing season. Do not over-fertilize young plants.