What happens if you do a 'sudo modprobe i2c_hid' from within the live environment? Which iso did you try exactly, 18.04 or 18.04.5? Can you also check with the latest 'ubuntu-20.04.2.0-desktop-amd64.iso'?
Just a standard Lubuntu 18.04.5 install, no changes besides the mentioned loading of ic2_hid, hwe-kernel 5.4 (same as in Ubuntu 20.04).
I don´t have the machine at hand to do further testing right now.
Found this thread while looking for a solution for the same problem. What worked for me was forcing the system to load the i2c_hid kernel module.
Quick test: "modprobe i2c_hid" => touchpad started working immediately.
For a permanent solution add a respective config line containing "i2c_hid" in...