list of custom post by custom field in frontend

The main issue is that you’ve mixed up two methods of querying posts.

You’re querying the correct posts here:

$posts = get_posts(array(
    'numberposts'   => -1,
    'post_type' => 'assessment',
    'meta_key'  => 'customer',
    'meta_value'    => $current_user_id
));

But then the posts you’re actually looping through are queried here:

$the_query = new WP_Query( $args );

Where $args is undefined and has nothing to do with the previously queried posts. You can pass the same arguments to WP_Query as get_posts(), but with posts_per_page, rather than numberposts:

function lista_mis_valoraciones_shortcode() {
    $current_user_id = get_current_user_id();
    $the_query       = new WP_Query(
        array(
            'posts_per_page' => -1,
            'post_type'      => 'assessment',
            'meta_key'       => 'customer',
            'meta_value'     => $current_user_id,
        )
    );

    if ( $the_query->have_posts() ) {
        while ( $the_query->have_posts() ) : $the_query->the_post();
            ?>

            <a href="<?php the_permalink(); ?>">
            <img src="<?php the_field( 'event_thumbnail' ); ?>" />
            <?php the_title(); ?>

            <?php
        endwhile;
    }

    wp_reset_postdata();
}
add_shortcode( 'lista_mis_valoraciones', 'lista_mis_valoraciones_shortcode' );

Note the other changes I made:

• You had mixed in HTML with PHP with the <img> and <a> tags. To output HTML you need to close the PHP tags with ?> and open them again with <?php when you’re done.
• You had a stray endif that needed to be removed.
• wp_reset_postdata() is more appropriate in this case than wp_reset_query().