My code here is just a total guess, but how can I tell the javascript to apply a style to the element I've specified?
No jQuery please. Just plain old vanilla.
var sheet = document.createElement('style')
sheet.innerHTML = "DIV(1) > OL(0) > LI(1) {background-color: blue;}";
document.body.appendChild(sheet);
<div>
<ul>
<li>1</li>
<li>2</li>
<li>3</li>
</ul>
<ol>
<li>1</li>
<li>2</li>
<li>3</li>
</ol>
</div>
<div>
<ul>
<li>1</li>
<li>2</li>
<li>3</li>
</ul>
<ol>
<li>1</li>
<li>2</li>
<li>3</li>
</ol>
</div>
DIV:nth-of-type(2) OL:nth-of-type(1) LI:nth-of-type(2).