Oh yeah, this can spread. Depending on the type of fungi, spores can be shot from 1 to 10 meters away (3 and 30 feet).
If it is an opportunistic pathogen it could be harmful. Might be a wise idea to cut the area off and remove all traces of the fungus and burn the removed parts.
I'm not by any means saying that all fungi are pathogen, far from it. Actually, less than 1% of known fungi are pathogens but, given that you have lilacs in the immediate vicinity, might be better to ere on the safe side.