UPDATE: April 2019 -> DisplayLink with kernel > 5.0.5 also works.
UPDATE: March 2019 -> DisplayLink with kernel > 4.18.20
It is now possible to install the driver with new versions of kernels.
I am writing this after updating to 4.20.13
You will have to use a script, however, which you can obtain from HERE (Github).
Once you have the script, remove the currently installed driver/module and install the new version. Script will download all dependencies for you. To remove old/install new apply the below steps:
sudo ./displaylink-debian.sh --uninstall
sudo dkms remove evdi/1.6.0 --all -q
sudo systemctl stop dlm.service
sudo systemctl disable dlm.service
sudo rm -f /lib/systemd/system/dlm.service
sudo rmmod evdi
sudo displaylink-debian.sh --install
February 2019 -> Ubuntu 18.04 LTS
Download driver from HERE. Then unzip, make sure it's runable and install (change the below file names to your versions):
$ unzip DisplayLink USB Graphics Software for Ubuntu 4.4.zip
$ chmod 775 displaylink-driver-4.4.24.run
Thats it! Once installed you can connect your DisplayLink to the PC and it should fly.
Make sure you have dkms installed on your system.
$ sudo dpkg -l | grep dkms
ii dkms 2.3-3ubuntu9.2 all Dynamic Kernel Module Support Framework
Also note, it works perfectly with the 4.15.0-45-generic kernel. However, I tried with the newest kernel 4.20 and the driver will not work - evdi for dkms will not compile. I haven't tried other kernels - if I try I will update the answer - but beware of this issue!
You can check your current kernel like this:
$ uname -r
Ok, so I decided to try some kernels and it seems that 4.18.20-041820-generic is the most recent working. Nothing higher worked for me.