The rule of thumb is to transplant shrubs in the dormant season when they are not in active growth.
When you dig them up it is best to get as much of a root ball (undisturbed soil) around the roots as possible to minimise stress to them and get them in a prepared hole quickly as not to allow any exposed roots to dry out in the air.
If they show signs of leaf browning, wilting or drop after the move, cut back the shrub so the root system has less foliage to deal with. This shouldn't happen, and only really happens if you have to move a shrub in the growing season. Hope this helps.

I assume that your plant has dropped its leaves by now. If not, wait until it does so. Lilacs can be successfully transplanted anytime before spring green up. You have some leeway in your climate zone.