Add custom classes to anchor in wp_nav_menu

You can do this with the nav_menu_link_attributes filter.

add_filter( 'nav_menu_link_attributes', 'wpse156165_menu_add_class', 10, 3 );

function wpse156165_menu_add_class( $atts, $item, $args ) {
    $class="class"; // or something based on $item
    $atts['class'] = $class;
    return $atts;
}