Index: src/js/_enqueues/wp/customize/nav-menus.js
===================================================================
--- src/js/_enqueues/wp/customize/nav-menus.js	(revision 57691)
+++ src/js/_enqueues/wp/customize/nav-menus.js	(working copy)
@@ -1664,6 +1664,8 @@
 			$reorderNav = control.container.find( '.menu-item-reorder-nav' );
 			$reorderNav.find( '.menus-move-up, .menus-move-down, .menus-move-left, .menus-move-right' ).on( 'click', function() {
 				var moveBtn = $( this );
+				control.params.depth = control.getDepth();
+
 				moveBtn.focus();
 
 				var isMoveUp = moveBtn.is( '.menus-move-up' ),
@@ -1677,8 +1679,19 @@
 					control.moveDown();
 				} else if ( isMoveLeft ) {
 					control.moveLeft();
+					if ( 1 === control.params.depth ) {
+						control.container.find( '.is-submenu' ).hide();
+					} else {
+						control.container.find( '.is-submenu' ).show();
+					}
 				} else if ( isMoveRight ) {
 					control.moveRight();
+					control.params.depth += 1;
+					if ( 0 === control.params.depth ) {
+						control.container.find( '.is-submenu' ).hide();
+					} else {
+						control.container.find( '.is-submenu' ).show();
+					}
 				}
 
 				moveBtn.focus(); // Re-focus after the container was moved.
Index: src/wp-includes/customize/class-wp-customize-nav-menu-item-control.php
===================================================================
--- src/wp-includes/customize/class-wp-customize-nav-menu-item-control.php	(revision 57691)
+++ src/wp-includes/customize/class-wp-customize-nav-menu-item-control.php	(working copy)
@@ -69,18 +69,23 @@
 				<span class="item-title" aria-hidden="true">
 					<span class="spinner"></span>
 					<span class="menu-item-title<# if ( ! data.title && ! data.original_title ) { #> no-title<# } #>">{{ data.title || data.original_title || wp.customize.Menus.data.l10n.untitled }}</span>
+					<# if ( 0 === data.depth ) { #>
+						<span class="is-submenu" style="display: none;"><?php _e( 'sub item' ); ?></span>
+					<# } else { #>
+						<span class="is-submenu"><?php _e( 'sub item' ); ?></span>
+					<# } #>
 				</span>
 				<span class="item-controls">
 					<button type="button" class="button-link item-edit" aria-expanded="false"><span class="screen-reader-text">
 					<?php
 						/* translators: 1: Title of a menu item, 2: Type of a menu item. */
-						printf( __( 'Edit menu item: %1$s (%2$s)' ), '{{ data.title || wp.customize.Menus.data.l10n.untitled }}', '{{ data.item_type_label }}' );
+						printf( __( 'Edit menu item: %1$s (%2$s)' ), '{{ data.title || data.original_title || wp.customize.Menus.data.l10n.untitled }}', '{{ data.item_type_label }}' );
 					?>
 					</span><span class="toggle-indicator" aria-hidden="true"></span></button>
 					<button type="button" class="button-link item-delete submitdelete deletion"><span class="screen-reader-text">
 					<?php
 						/* translators: 1: Title of a menu item, 2: Type of a menu item. */
-						printf( __( 'Remove Menu Item: %1$s (%2$s)' ), '{{ data.title || wp.customize.Menus.data.l10n.untitled }}', '{{ data.item_type_label }}' );
+						printf( __( 'Remove Menu Item: %1$s (%2$s)' ), '{{ data.title || data.original_title || wp.customize.Menus.data.l10n.untitled }}', '{{ data.item_type_label }}' );
 					?>
 					</span></button>
 				</span>