This was found on the trunk of a friends lilac.
It's what is commonly known as a bracket or shelf fungus - they all are polypores and this group of fungi is fairly similar one to another in structure, but in outward appearance they come in a range of colours and sizes. When this occurs on a tree, it means the heartwood of the tree has been infiltrated already by the mycorrhizae - what you see on the outside are the fruiting bodies. I'm afraid this means the tree is on its way out - your friend should check how stable the tree is by pushing on the trunk to see if it's still firm,and it should be checked ongoing if he does not want to remove it now. The danger from it over time is that it might fall, and if it's near a property, building or where people walk regularly, that might mean significant damage.
If these have appeared near the base of the tree, its probably best to remove it quite quickly - higher up the trunk might mean it lasts a bit longer, but not necessarily.
As you say ; a fungus = mushroom ( which I don't recognize ). However , that trunk of the lilac is likely dead and does not know it yet. I would cut that trunk to try to reduce growth of the fungus into the rest of the bush. The lilac will likely come back very well if pruned while dormant ( winter).