By default, Nav Menu widget of Elementor Pro has nav menu items align option that can’t be set individually to the tablet and mobile views.

Here is the solution:
<?php // Some Other Codes add_action('elementor/element/nav-menu/section_layout/before_section_end', function ($instance, $args) { $instance->add_responsive_control( 'responsive_align_vertical', [ 'label' => __('Alignment', 'elementor'), 'type' => \Elementor\Controls_Manager::CHOOSE, 'options' => [ 'flex-start' => [ 'title' => __('Left', 'elementor'), 'icon' => 'fa fa-align-left', ], 'center' => [ 'title' => __('Center', 'elementor'), 'icon' => 'fa fa-align-center', ], 'flex-end' => [ 'title' => __('Right', 'elementor'), 'icon' => 'fa fa-align-right', ], ], 'condition' => [ 'layout' => 'vertical', ], 'selectors' => [ '{{WRAPPER}} .elementor-nav-menu a' => 'justify-content:{{VALUE}};', ], ] ); $instance->add_responsive_control( 'responsive_align_horizontal', [ 'label' => __('Alignment', 'elementor'), 'type' => \Elementor\Controls_Manager::CHOOSE, 'options' => [ 'flex-start' => [ 'title' => __('Left', 'elementor'), 'icon' => 'fa fa-align-left', ], 'center' => [ 'title' => __('Center', 'elementor'), 'icon' => 'fa fa-align-center', ], 'flex-end' => [ 'title' => __('Right', 'elementor'), 'icon' => 'fa fa-align-right', ], ], 'condition' => [ 'layout' => 'horizontal', ], 'selectors' => [ '{{WRAPPER}} .elementor-nav-menu__container' => 'justify-content:{{VALUE}};', ], ] ); }, 99, 2); ?>
Add the above code somewhere in your functions.php file or somewhere appropriate.