Well, it only took me less than 24 hours. The answer is: that if you have fungi growing on your tree, then your tree isn't necessarily dead. It could be, or it might not me.
Here's the skinny:
What seems to be the most damaging fungal infections of plants are fungal vectors that are transferred to plants by insects. With Picea abies and Abies spp (Norway Spruce and True Fir) wood wasps intoduce fungi into damaged wood via exuded sap from wounds in the tree. The wasps are attracted to the sap and fungi are introduced into the tree from the waps bodies (presumably).
Now, in this particular study; researchers examined wounds on trees that were up to 24 years old and had fungal growths inside the trees with wasp larvae growing in the fungal (for lack of a better word: tubes).
Anyway, I don't want to review the entire article but, here is a fundamental rule of thumb in biology: A parasite is only a good parasiteif it does not actually kill it's host.
I mean, that would make sense, if a fungus killed it's tree host, then it would probably die as well or at very least have to find a new host.
With regard to fruiting bodies (aka: mushrooms). Well, mushrooms are not the only way that fungi as whole disperse themselves but, if you have fruiting bodies growing on some wood, it does not mean that the wood is dead, it means that the wood is infected and the fungus that has infected the wood is reproducing.
Now, the study that I have been quoting does make note that the heartwood of the plants was eventually damaged or destroyed so yes, death is often emminant if something is not done to curtail the disease (and plants can do this (refer to the post on Secondary Metabolites (terpenes). Anyway, overtime severe damage can occur. Best to nip the problem at the bud when you first noticed a problem
With regard to the above mentioned Lilac, Yes an excellant way to stem the spread of this fungus would be to cut away the infected areas and bud out new shoots. But, the infected areas are not necessarilly dead, what most likely happend is that when the tree was damaged, it exuded some sort of sap to put a "band aid" over the wound which attracted some sort of insect deposited the fungi or perhaps the fungal spore in the air stuck to the exudant and the fungus started assexually reproducing (growing) and voila, there is your mildew.