Thank you for your inquiry, and for mentioning the possibility that your shrub may have been exposed to a lawn herbicide. The fact that your hostas died within two weeks is a hint that some type of herbicide is likely the culprit for the injury to your lilac shrub.

Herbicide plant damage can arise in a variety of forms. It is usually the result of unintentional contact with chemicals from spray drift or contact with vapor. Recognizing accidental herbicide injury may be difficult as the symptoms can mimic other plant conditions.

The type of injury can be determined by the time symptoms begin to show. Problems that appear right after new plants begin to germinate are often the result of carry-over from previous applications, high rates of application, shallow planting, and even poor timing.

Herbicide plant damage that appears on mature plants may be due to drift, misapplication, high temperatures or humidity, or incorrect treatment.

The signs of injury will depend on the type of herbicide which contacted the plant. Post-emergence (that is, after foliage, etc. has already appeared on the  plant) broadleaf herbicides are responsible for most injuries. These result in twisted leaves, cupped foliage, narrower new leaves, and  roots that appear on the surface in annual plants. On ornamental grasses, these products cause yellowing and die back.

Non-selective herbicides will cause accidental herbicide injury in many instances and these controls must be applied according to directions and with caution. Symptoms of herbicide injuries from these products include yellowing in leaves, die back, and general ill health in plants that might have been  exposed. In some cases, fixing herbicide spray drift is possible if it is caught early enough.

You may wish to contact your lawn care company to inquire what ingredients  were used near your shrub. Since the lilac shrub is attempting to leaf, and has complete die-back appears only on part of the plant, it is possible that the injury is not permanent. It is unlikely that flowers will appear this year.

The following links which list symptoms, causes, and recovery options may help you.
https://hnr.k-state.edu/extension/horticulture-resource-center/common-pest-problems/documents

/Herbicide%20Damage%20to%20Trees%20Shrubs%20Turf%20and%20Garden%20Plants.pdf
https://www.extension.purdue.edu/extmedia/ID/ID_184_W.pdf

https://hortnews.extension.iastate.edu/chemical-injury-garden-plants