How do I run Mailman on a server with an external MTA?
Using an external MTA for outgoing mail from Mailman is fairly straightforward.
There are configuration settings for SMTPHOST and SMTPPORT to specify where to connect to send mail and beginning with 2.1.23 there are settings SMTP_AUTH, SMTP_USER, SMTP_PASSWD and SMTP_USE_TLS to provide authentication and use TLS with the external MTA.
Getting mail from the external MTA to Mailman is more complex.
This article describes a method using fetchmail, and this blog post by Jesus Cea describes another setup in detail.