Add login hyperlink to secondary navigation menu

You could do this with a filter on wp_get_nav_menu_items.

In this example, we first check if it’s the admin screen or the user is not logged in, and bail out if that’s the case.

Then we look at each menu item and find the one with Log In as the menu item title, and unset it.

function wpa_remove_menu_item( $items, $menu, $args ) {
    if( is_admin() || ! is_user_logged_in() ) return $items;

    foreach ( $items as $key => $item ) {
        if ( 'Log In' == $item->title ) unset( $items[$key] );
    }
    return $items;
}
add_filter( 'wp_get_nav_menu_items', 'wpa_remove_menu_item', 10, 3 );