I keep on trying different distributions on my E15 Gen 2 laptop.
First thing is always to install a recent kernel that will not prevent the system coming back from sleep mode. It can be done by following instructions for Ubuntu wiki or using the mainline application (continuation of the free version of ukuu).
The Function keys are working after computer went to sleep mode. Here is a way to get the computer to go in sleep mode and wake up automatically at boot.
The rtcwake command enters a system sleep state until specified wakeup time. it is part of util-linux package on ubuntu based distributions, so install it if it is not done already:
sudo apt install util-linux
Then modify the root crontab:
sudo crontab -e
Add this line to the file:
@reboot sudo rtcwake -m mem -s 2
Save the file.
This will put the computer in sleep mode for 2 seconds after boot.
Reboot your computer and login into your user session the Function keys should be working.