Dawn said:

our next door neighbor pruned the lilac bush that grows on the
property line and dropped the branches over the fence into our yard.
(Probably sometime last fall or early winter)

Anyway, I think he's perfectly within his right to whack off whatever
part of the plant he feels is invading his yard, but if he's going to
do that he can take care of the debris himself. Has anyone else had
to deal with this sort of problem?

Let me present a different viewpoint, since everyone thinks your neighbor
was in the wrong... You neglected to properly prune your Lilac to the
point your neighbor had no choice but to prune it himself as it was
invading his property; furthermore, you have neglected upkeep in your yard
that you don't even know when this happened but you suspect last fall.
IMO, it is you that is clearly in the wrong and you should clean up the
mess and maintain your property in a more respectful manner.
--
Sincerely,
The Vice President