The /var directory is the normal directory for server logs ( /var/log to be exact ).
The logs aren't generated by Listmail but rather by your MTA ( Your email program:  Sendmail, Qmail, etc ).
Couple options:  1)  Disable logging - Definitely not recommended
2)  Make sure your server rotates logs daily and compress the old ones, check /etc/logrotate.conf
3)  You should be doing #2 for sure, but maybe you need a bigger drive or more space in /var