Can you give a user access to manage his mail lists for his domain?

you mean by enabling mailman in features and then adding it to his domain?
I suppose yes. That seemed to have worked for me anyway once i got mailman running

Yes, as ronald mentioned, you can grant virtual server owners access to the Mailman mailing lists for their domain--and grant them the ability to create new ones.

If you didn't install Virtualmin using our install script, you may not have the Mailman plugin module, however. It's required for this task, so you'll need to install it and configure it. You also need Mailman to be installed and working, obviously.