Let me clarify the situation.
Below is the HTML code:
<ul class="children">
<li class="bypostauthor">
This particular image should have borders:
<img width="67" height="67" src="http://i.imgur.com/BRUVD7s.jpg">
<ul class="children">
<li>
This image, however, should NOT have borders:
<img width="67" height="67" src="http://i.imgur.com/BRUVD7s.jpg">
</li>
</ul>
</li>
</ul>
Regarding the CSS section:
.bypostauthor img{
border:5px solid red;
}
The objective is to apply a border to the image in the list with the class bypostauthor, not to the image within its nested list.
You can view an example on this fiddle link.
Regrettably, it's not possible to assign a unique class to the individual images. Only to their parent list element.