Adapted a Wordpress custom walker to add <i> & icon classes within <a> of the menu using native 'custom classes' interface.

functions.php

<?php

  class description_walker extends Walker_Nav_Menu
  {
  
    function start_el(&$output, $item, $depth, $args)
    {
         global $wp_query;
         $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';
  
         $class_names = $value = '';
  
         $classes = empty( $item->classes ) ? array() : (array) $item->classes;
  
         $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) );
  
         preg_match("/icon[^\s]*|icon/", $class_names, $icons);
  
         $class_names = preg_replace("/icon[^\s]*|icon/", "", $class_names);
  
         $class_names = ' class="'. esc_attr( $class_names ) . '"';
  
         $output .= $indent . '<li id="menu-item-'. $item->ID . '"' . $value . $class_names .'>';
  
         $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
         $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
         $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
         $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';
  
         $prepend = '<i class="' . $icons[0] . '"/></i>';
         $append = '';
         $description  = ! empty( $item->description ) ? '<span>'.esc_attr( $item->description ).'</span>' : '';
  
         if($depth != 0)
         {
                   $description = $append = $prepend = "";
         }
  
          $item_output = $args->before;
          $item_output .= '<a'. $attributes . '>';
          $item_output .= $args->link_before .$prepend.apply_filters( 'the_title', $item->title, $item->ID ).$append;
          $item_output .= $description.$args->link_after;
          $item_output .= '</a>';
          $item_output .= $args->after;
  
          $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
  
                      if ($item->menu_order == 1) {
              $classes[] = 'first';
          }
  
      }
  }

?>

header.php

<?php

    $header_args = array(
        'theme_location'  => 'header_menu',
        'container'       => 'nav',
        'container_class' => 'header-menu',
        'echo'            => true,
        'items_wrap'      => '<ul id="%1$s" class="%2$s">%3$s</ul>',
        'depth'           => 1,
        'walker'          => new description_walker()
    );

?>