HI!

Here is an example for adding a menu item with your's code:

function thegem_menu_new_menu_item($items, $args){
    if($args->theme_location == 'primary' && thegem_get_option('header_layout') !== 'overlay'){
        $items .= '<li class="menu-item menu-item-NEW"><a href="#link">link</a></li>';
    }
    return $items;
}
add_filter('wp_nav_menu_items', 'thegem_menu_new_menu_item', 10, 2);

You are welcome!