Custom walker nav – Add sequential number as class

Try it like this:

class ik_walker extends Walker_Nav_Menu {

    function start_lvl(&$output, $depth) {
        $GLOBALS['ik_walker_counter'] = 0;
        $output .= '<nav class="site-navigation" role="navigation">'.
            '<ul>';
    }

    function end_lvl(&$output, $depth) {
        $output .= '</ul>'.
            '<button id="menu" class="menu-button" type="button" role="button" aria-label="Menu Toggle">'.
            '<span class="icon-menu"></span>'.
            '</button>'.
            '</div>';
    }

    function start_el(&$output, $item, $depth, $args) {
        global $wp_query;
        global $ik_walker_counter;
        $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 ) );
        $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        ) .'"' : '';
        $attributes .= ' class="c'.(++$ik_walker_counter).'"';
        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        if(strlen($item->description)>2){ $item_output .= '<br /><span class="sub">' . $item->description . '</span>'; }
        $item_output .= '</a>';
        $item_output .= '<span class="'.$args->my_individual_class.'"></span>';
        $item_output .= $args->after;
        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }

}

Your c1 through cn classes are tracked/counted by the global $ik_walker_counter variable, which is reset every time we start a new level. The individual class goes as new parameter in your walker arguments ( e.g., 'my_individual_class' => 'paw-icon'.