I am assuming that you have root access on the server without which the following instructions won't work.
First you have to cd to the directory corresponding to your mailing list. All mailing list settings will be kept at
Each mailing list will have a folder with the name created by replacing the '@' with a '.'. So [email protected] will have a folder list.example.com. So cd to the folder with the correct folder name. Replace list.example.com in the example below.
The configuration will be kept in a file config.pck. This can be read by the dumpdb utility that comes with mailman. You can run this as follows
../../bin/dumpdb -p config.pck | less
Now you could really take it to the next level and parse the output and read just the settings corresponding the member list but the above worked well for me. Do note that the paths correspond to a WHM/Cpanel server running CentOS.