Note: this only applies to VPS, Semi-dedicated, or Dedicated Server plans. If you need mailing lists exported from a Shared Hosting account, please contact support.
Find the mail lists by looking in '/usr/local/cpanel/3rdparty/mailman/lists/'
Once you find the mail list's name, change to the following directory:
Run the export command and add the mail list's name at the end (i.e. mail list's name is 'mailing.yourdomain.com'):
./list_members -f -o mailing-info.txt mailing.domian.com
-f puts the 'fullnames' in the output file
-o is the name/destination/location of the output file