I noticed the "class" parameter used as described here has no effect on the resulting HTML code. In other words,
..has no effect, using the default plugin installation.
I found that the plugin uses a default.php template installed under the themes/ folder (i.e. not the default.php template in the plugins/ folder). The problem is the default.php template lacks code to utilize the "class" parameter.
I fixed this in the template by changing line 41 to:
$lcp_display_output .= '<ul class="lcp_catlist ' . $this->params['class'] . '">';
This appends any class you set as a parameter to the existing class. Hope this helps someone.