How can I alter a MenuItem on the Options Menu on Android?

For this type of operation I usually choose not to alter the menu items, but just hide the ones you don’t need:

@Override
public boolean onPrepareOptionsMenu(Menu menu) {
    super.onPrepareOptionsMenu(menu);
    menu.findItem(R.id.start).setVisible(!isStarted);
    menu.findItem(R.id.stop).setVisible(isStarted);
    return true;
}