One other way involves adding a custom argument to the wp_nav_menu() function. This is handy if you need to pass a value from outside of the walker class altogether:
wp_nav_menu( array(
'theme_location' => 'secondary',
'depth' => 1,
'walker' => new Custom_Walker(),
'walker_arg' => 'Custom argument value here'
) );
From within the walker class you can then access this custom arg from within start_el() function inside of the walker class (Walker_Nav_Menu::start_el()) like this:
$custom_arg = esc_attr( $args->walker_arg );