I’ve been looking for the same thing, I think I’ve got the answer 2/3rds of the answer…
First, define a custom template for the plugin;
https://github.com/picandocodigo/List-Category-Posts/wiki/Template-System
Within that template, you can build up your output (containing element/s + per item) by building up the (as per demo template’s examples). It turns out you can also access default WordPress functions in these lists..
$lcp_display_output .= "<li>";
$lcp_display_output .= '<a href=\"' . get_permalink($post->ID) . '\">';
$lcp_display_output .= $this->get_thumbnail($post);
$lcp_display_output .= $this->get_post_title($post, 'h3');
...
$lcp_display_output .= "</a>";
$lcp_display_output .= "</li>";
This is where you build up your desired styling.
Then, in your post, specify you don’t want the titles to act as links (you can dress them up with tag & class at the template level);
[catlist name="cat1" template=your-template-name thumbnail=yes link_titles=false]
Where this falls over is that it still returns the thumbnail as a formatted link. I can’t see a way to bring it back as just the thumbnail src via the plugin:
https://github.com/picandocodigo/List-Category-Posts/blob/master/doc/FAQ.md#no_link
This is my first bit of WordPress code though, so I’m sure there’s a way to get it from the built-in WordPress functions.