Consider the following change to avoid many entrances to the lock

    if (LastFired.Add(FireDelay) < DateTime.UtcNow)
    {
        lock (_sync)
        {
            if (LastFired.Add(FireDelay) < DateTime.UtcNow)
            {
                LastFired = DateTime.UtcNow;
                GeneralDirectoryChanged.Invoke(System.IO.Path.GetDirectoryName(fullPath));
            }
        }
    }