Please be aware that Lié only supports macOS 10.10 until 10.14 and Windows 10. Don't try to flash the firmware from a non-compatible device. It won't work and could (at least temporarily) brick your unit.
The update process is stuck at "Finalizing update" for more than just a few seconds, and the LEDs on Touché (SE) are white again? To proceed, please put your unit into Sleep Mode via pressing the Encoder for 2 seconds. Then, wake it up again by clicking on any Button. The procedue will move on to the "unplug" and "replug" requests.
If "Please replug the device" still shows, despite already having unplugged and replugged the unit, please just unplug, wait a few seconds and replug again.
Your unit's LEDs don't turn pink when triggering the firmware update form Lié via Menu -> Settings -> Install firmware ?
Close Lié, manually force Touché (SE) into Bootloader Mode via pressing and holding the two Buttons and the Encoder at the same time, while plugging the unit to your computer. All four LEDs on your unit should turn pink, indicating it is in Bootloader Mode.
The procedure is shown here: https://www.dropbox.com/s/etwjffpz76jece5/Touch%C3%A9_BootloaderMode.mov?dl=0
If all advice given above doesn't help, please delete Touché (SE)'s driver entries from your computer, in order to start from scratch. Read this article to learn how it is done:
How can I reinstall the Touché (SE) driver if my unit is not recognized correctly?