I found an issue with Internet Explorer 9 and Webmail Lite. In js/commons/functions.js on line 322 IE9 will throw an error and stop processing. This currently happens on your demo site as well. The issue only occurs in IE9 and happens in the following function.
 
function CreateChildWithAttrs(parent, tagName, arAttrs)
{
 var node;
 if (Browser.IE) {
  var strAttrs = '';
  var attrsLen = arAttrs.length;
  for (var i = attrsLen - 1; i >= 0; i--) {
   var t = arAttrs[i];
   var key = t[0];
   var val = t[1];
   strAttrs += ' ' + key + '="' + val + '"';
  }
  tagName = '<' + tagName + strAttrs + '>'
  node = document.createElement(tagName);
 }
 else {
  node = document.createElement(tagName);
  var attrsLen = arAttrs.length;
  for (var i = attrsLen - 1; i >= 0; i--) {
   var t = arAttrs[i];
   var key = t[0];
   var val = t[1];
   node.setAttribute(key, val);
  }
 }
 parent.appendChild(node);
 return node;
}
 
 
If you alter the first if to check the browser version as well like this
 
function CreateChildWithAttrs(parent, tagName, arAttrs)
{
 var node;
 if (Browser.IE && Browser.Version < 9) {
  var strAttrs = '';
  var attrsLen = arAttrs.length;
  for (var i = attrsLen - 1; i >= 0; i--) {
   var t = arAttrs[i];
   var key = t[0];
   var val = t[1];
   strAttrs += ' ' + key + '="' + val + '"';
  }
  tagName = '<' + tagName + strAttrs + '>'
  node = document.createElement(tagName);
 }
 else {
  node = document.createElement(tagName);
  var attrsLen = arAttrs.length;
  for (var i = attrsLen - 1; i >= 0; i--) {
   var t = arAttrs[i];
   var key = t[0];
   var val = t[1];
   node.setAttribute(key, val);
  }
 }
 parent.appendChild(node);
 return node;
}
 
everything works as intended. It appears the IE9 has changed the way they do some things. Hope this is helpfull.