Here is some starting points that might help:
First, you will be parsing XML to JSON on the server-side ( using PHP I assume ). These are starting points to do that:
Once you have PHP doing that, You need to point your JavaScript to it to get your JSON. You can do by using AJAX. If you are already using jQuery on your site, then you can use jQuery.ajax()
Doing that, you will end up with an array of all the elements you want to update on your client-side and you just need to iterate over them, and replace the content of each <li>
based on their id
Google is your friend to find more specifics as you go :)