The mail, web and DNS server has received new disks. The old 5400RPM 320Gbytes HDDs have been replaced by 1Tb SSD disks. This will allow to use larger quotas on the mail-server side, and will be specially faster for all requests that are ran on the server.

The day after the OS has been upgraded from Ubuntu 14.04 LTS to Ubuntu 18.04 LTS getting through Ubuntu LTS 16.04 LTS.
The main issues have been the passage from upstart to systemd, where some applications (mysql)_ could not be upgraded correctly as the upgraded needed to run mysql_upgrade, but the upgrader did shut down mysql for the process. Hence - stopping the upgrader just after he stopped the mysql-server, in another terminal, starting the mysqld, and then sending the CONT signal to the ugprader made the trick.
The second issue was apparmor and some applications not working correctly (bind9), had to be fixed by adding some special paths for bind9 to gather its data.
The mysql DB 5.7 is crap. Most application stopped working with it. Luckily I noticed that my dev environment using Mariadb 10.1 worked, so I tried upgrading the DB to mariadb 10.3 (10.2+ is required, as previous versions would not be compatible with mysql 5.7). That upgraded, all apps worked as before.
Luyckily dovecot, postfix, opendkim and the greylisting stuff were not impacted by the upgrade. Apparently admins of these installations don't like upgrades to mess with all this.
Lessons learned: Next developments will make sure the applications are running inside docker containers. This way - an OS Update will not impact any of the settings.