Skylla recently set up Ubuntu 18.04 on the new Thinkpad P1 Gen 2 and had some issues with no WiFi drivers after install. Looking for a fix I found this Stack Overflow answer which pointed to the wireless driver issues. They suggested upgrading to Ubuntu 19.04 but this is not an option for work, we need the Long Term Support version.
Instead to get this working on Ubuntu 18.04 you can install a newer kernel with:
sudo apt install linux-generic-hwe-18.04-edge
After this installs reboot and WiFi should be up!