ajaxurl is set only in admin. If this is a frontend ajax (looks like it due to nopriv), you have to localize the script on enqueueing:

    add_action( 'admin_enqueue_scripts', 'my_enqueue' );
    function my_enqueue($hook) {
        if( 'index.php' != $hook ) return;	// Only applies to dashboard panel
            
    	wp_enqueue_script( 'ajax-script', plugins_url( '/js/my_query.js', __FILE__ ), array('jquery'));
    
    	// in javascript, object properties are accessed as ajax_object.ajax_url, ajax_object.we_value
    	wp_localize_script( 'ajax-script', 'ajax_object',
                array( 'ajax_url' => admin_url( 'admin-ajax.php' ), 'we_value' => 1234 ) );
    }

In the JS file, you can reach the ajax_url as a variable of ajax_object:

    jQuery.ajax(
            ajax_object.ajax_url, {
            action: 'lu_ajax',
            status: 'enabled'
            },
            success: function (a) {
            alert(a)
            }

See http://codex.wordpress.org/AJAX_in_Plugins