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