Hi,
You are almost there. You have already setup additional look items such as "second_level" and "third_level". However you need to associate these look items to the real menu items. "second_level" and "third_level" are not built-in looks items. So their name does not bare any special meaning. In another word, a look item will not be automatically applied to second level items just because you name it "second_level".
In order to associate an look item to the real menu item, you must set the menu item's LookID property. There are several ways to do this. You can specify it in your sitemap, then use a Binding object to map your XML attribute to "LookID" field, or you can handle the menu's ItemDataBound event and explicitly set it with code. You can find more information about these in the following topics:
http://doc.essentialobjects.com/library/1/menucommon/databinding/populate_datasource.aspxhttp://doc.essentialobjects.com/library/1/eo.web.navigationitem.dataitem.aspxOne more thing that may worth extra attention is, a "SubMenu" is a sub menu of its parent item. So in order to set the third level sub menu styles, you actually modify the second level item's "Sub menu", which means in this case the look item is applied to the second level item.
Thanks!