I have hard clay soil and my lilac is doing well. True, I have amended, and at the time, I think I just "amended the hole". It is a white lilac, "Madame Lemoine". I never "feed" it, though I have dug around it for other plants. Does your lilac get full sun? Mine gets a bit more than a half day, but intense sun during the summer. I do not have the room for more lilacs. This one produces more plants under the soil line, (suckers?), so I have to dig them out and give them away from time to time.
I cut it back every other year, so it does not get too tall. Some years I just get a few blooms, and other years there are many. I may have forgotten and cut back every year some years.