If someone comes across this thread because he/she has the same issues as me:
As @Kai pointed out in [comfoair|serial] ComfoAir binding (and other serial bindings) not working on PINE64 · Issue #4413 · openhab/openhab1-addons · GitHub the 32/64-bit problem can be solved by running OpenHAB using a 32-bit JVM.
On a PINE A64+ with Ubuntu 16.04 this can be done as follows:
sudo dpkg --add-architecture armhf
sudo apt-get update
sudo apt-get install openjdk-8-jre-headless:armhf
This will install a 32-bit JVM in /usr/lib/jvm/java-1.8.0-openjdk-armhf which you need to call in startup.sh so it is used instead of the default JVM. Then, the serial library works flawlessly.