Lilacs do not require too much Pruning - Here's how.
All that is normally required of a Syringa (Lilac), is the removal of faded flower. No more - unless you want to re-shape the bush. In the latter case, do it as you wish, right after flowering.
You may miss out on some flower the following year.
It is important to take off the old flower growth before it starts to set seed. This will then allow new shoots to form, which will be the flowering growths for the next year. The sooner you 'de-head' - the faded flowers, the better the following year's flowers will be.
Simply snip off the dead flower, just below the old flower stalk and above a pair of buds which will probably be starting to show though. A good clean cut with sharp secateurs will ensure quick healing and getting the new flowering growth moving.
All varieties of Lilac should be treated in this way. this includes the Syringa vulgaris, S. Hyacinthiflora types.