So I did find that you can add some capabilities to the editor role that opens up the Menu to the editor.
Add the following code to your theme function, and the editor will gain access to the menu, plus the following areas: Theme Options (but can not switch, edit or install themes), Menus, Background, Widgets and Custom Headers.
While I would still prefer to only provide access to the menus without the other items, this may be the fix you need.
// get the the role object
$role_object = get_role( 'editor' );
// add $cap capability to this role object
$role_object->add_cap( 'edit_theme_options' );