You'll have to be careful that you don't lose your ListMail data. When a domain name is removed from a hosting server the files, and MySQL data, are generally deleted automatically. In this case you will need to perform a MySQL "Export" from PhpMyAdmin, commonly accessible through your control panel, and download your ListMail data.
Once your new domain is set up, you can set up a new MySQL database, import your data, and upload the ListMail files to resume where you left off. Your ListMail configuration will should be changed to reflect the new domain name and email addresses. The "Send From" email can usually be anything you want but the bounce address should always be an address on the server/domain you are running ListMail on.