Theme development: How to add CSS classes to menu items?

You can use the nav_menu_css_class filter which is applied to every menu item in the specified nav menu.

add_filter('nav_menu_css_class' , 'special_nav_class' , 10 , 2);

function special_nav_class($classes, $item){
    $classes[] = 'your-custom-class';
    return $classes;
}

More info: http://www.wpbeginner.com/wp-tutorials/add-a-custom-class-in-wordpress-menu-item-using-conditional-statements/