Using CSS ::before to add a small icon before list links

Well, list-style-image is made for that.

Supported since IE 4.0. That should be enough I guess.

ul {
  list-style-image: url('http://placehold.it/12x12');
}
<ul>
  <li> Text content </li>
  <li> Text content </li>
  <li> Text content </li>
</ul>

There's no need to use the ::before pseudo-element here at all. You can just use a background image:

.list-menu {
  background-image: url('http://placehold.it/16x16');
  background-position: left center;
  background-repeat: no-repeat;
  padding-left: 20px; /* Adjust according to image size to push text across. */
}
<div class="sb-slidebar sb-left sb-style-push">
	<nav>
		<ul>
			<li class="list-menu"><a href="#">Home</a></li>
		</ul>
	</nav>
</div>