The problem is that you're including the jQuery script files more than once. Specifically, what's causing your problem is that you're loading jQuery once after the LavaLamp plugin has been loaded, thereby overwriting the definition of $
that had been extended with a plugin.
<!-- jQuery is first included here; $ is defined -->
<script type="text/javascript" src="sitefiles/jquery.js"></script>
<script type="text/javascript" src="sitefiles/easing.js"></script>
<script type="text/javascript" src="sitefiles/easingfix.js"></script>
<!-- then your LavaLamp plugin is included here; $.fn.LavaLamp is defined -->
<script type="text/javascript" src="sitefiles/lavalamp.js"></script>
<script type="text/javascript" src="sitefiles/imagecycle.js"></script>
...
<!-- Now, later on, jQuery is included again; $ is overwritten
and $.fn.LavaLamp is lost -->
<script type="text/javascript" src="js/jquery.min.js"></script>