You Save_Click event handler is not passed a LLS, but a context MenuItem. The DataContext of the MenuItem is the object you are after.
private void Save_Click(object sender, System.Windows.RoutedEventArgs e)
{
var element = (FrameworkElement)sender;
SoundData data = element.DataContext as SoundData;
_CustomRingtone.Source = new Uri(data.FilePath, UriKind.RelativeOrAbsolute**);
_CustomRingtone.DisplayName = "Ring";
_CustomRingtone.Show();
}