Solution - 1

<div id="mygallery" >
  <a rel="nofollow" href="path/to/myimage1_original.jpg">
    <img alt="Title 1" src="path/to/myimage1_t.jpg"/>
  </a>
</div>

<a rel="nofollow" href="#"><?php  the_post_thumbnail(); ?></a>

<a rel="nofollow" href="<?php echo wp_get_attachment_url( get_post_thumbnail_id(get_the_ID()))?>"><?php  the_post_thumbnail(); ?></a>

Solution - 2

Try this one. HTML id must be mygallery instead of #mygallery.

<div id="mygallery" >    

<?php 
    // the query
    $args = array(  'post_type' => 'images');
    $Justified_Query = new WP_Query( $args );
?>
<div id="main-content" class="main-content">
	<div id="primary" class="content-area">
    <div class="large-8 columns">
<div id="content" class="site-content" role="main">
      <div id="mygallery" >    
<?php  if ( $Justified_Query->have_posts() ) : ?>
  <?php while ( $Justified_Query->have_posts() ) : $Justified_Query->the_post(); ?>
    <a rel="nofollow" href="#"><?php  the_post_thumbnail(); ?></a>
  <?php  endwhile ?>
  <?php  wp_reset_postdata() ?>
<?php  else : ?>
  <p><?php  _e( 'Sorry, no posts matched your criteria.' ); ?></p>
<?php  endif; ?>

<!-- Justified Image Grid -->
     </div> <!--#mygallery-->

		</div><!-- #content -->
  </div><!-- Grid -->
	</div><!-- #primary -->
	<?php  get_sidebar( 'content' ); ?>
</div><!-- #main-content -->

<script language="Javascript">
(function($)
{
    $.ready(function()
    {
        $("#mygallery").justifiedGallery();
    });
})(jQuery);        
</script>

Solution - 3

I have had issues with javascript jquery before, I have gotten other jquery scripts to work in the past by trying to include the js file in different places in the header.php file instead of with enque scripts and it has worked. Moving it below or above other .js files can make a difference sometimes. Good luck.

Solution - 4

Change

 
<div id="#mygallery" > 

<div id="mygallery" >