If you only need to add a “lightbox” class to each element you just need to change this :
echo'<div class="mix '.$item_classes.'">'.get_the_post_thumbnail().'</div>';
to this :
echo'<div class="mix lightbox '.$item_classes.'">'.the_post_thumbnail('thumbnail', array('class' => 'lightbox')) .'</div>';
And if you want to add the full size image to be opened, try this :
$featured_img_url = get_the_post_thumbnail_url(get_the_ID(),'full');
echo'<div class="mix lightbox '.$item_classes.'"><a href="' . esc_url($featured_img_url) . '">' . the_post_thumbnail('thumbnail', array('class' => 'lightbox')) .'</a></div>';
check this for all the sizes available