Personally I’d do the following:

• boot into the bios config menu to make sure it’s unlocked (if it’s locked and they don’t have the password that’d be a dealbreaker for me)
• boot into a live linux environment from usb and test both batteries, keyboard, trackpoint/trackpad, speakers, microphone, wifi, and all external ports (T480 has 2 usb-c, 2 usb-a, ethernet, hdmi, headset, and sd - make sure batteries charge well from both usb-c ports)
• to check the storage health, install nvme-cli if not installed, run nvme smart-log /dev/nvme0 and check the “percentage_used” value: if it’s near 100% it might die and need replacement soon
• to check that the vents, airflow, and cooling hardware are in good shape, install stress if not installed, run stress -c 7 to load up 7 of the 8 available cpu threads, make sure the fan spins up good and strong, and watch /sys/class/thermal/thermal_zone0/temp to make sure the cpu temperature stays under ~90-95 degrees

On my own time later, I’d run memtest86+ overnight from bootable usb to check the memory, then install tlp and run tlp recalibrate with the laptop on the charger to recalibrate the batteries

Edit: enjoy the new laptop! I hope it works great for you