Mark,
If your Lilac has shown any signs of die back (and I would expect your shrub to be affected by now) GET RID OF IT PRONTO !
I had Lilac in one of the gardens I used to look after and Lilac were one of the first shrubs to suffer when the dreaded Honey Fungus decided to take up residence.

This
WILL spread to other shrubs and trees in your garden and kill them too, so do the hard work now to save yourself having to do 3 times or more hard work in the future - DIG IT UP, ROOTS an' ALL.
BUT, if the Lilac seems completely healthy, wait until next year and keep a close eye on it. It is normal after pruning for a tree or shrub to die back to a healthy joint, but if a whole shoot/branch dies back to the ground, I would fear the worst and dig it up with as much of the root system as possible and burn it.
Other sources of information will tell you Honey Fungus will only affect shrubs and trees under stress of some sort (a wound or drought conditions or too much water) but in my 10 years of personal experience fighting Honey Fungus, THIS IS RUBBISH ! (and so is Armillotox which has now been taken off the market for certain uses)
Neil.
Silly me, I note you have already said at the beginning it has died for no apparent reason - the Honey Fungus HAS killed it, so start digging Mark - it'll keep you fit.