Please be aware that Lié only supports macOS 10.11 until 10.15 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.
Your unit's LEDs don't turn pink by themselves when triggering the firmware update from Lié via Menu -> Touché (SE) -> 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 now turn pink, indicating it is in Bootloader Mode.
If you're using Lié as plugin inside a DAW or if you have a DAW open in the background while trying to perform the firmware update, it might prevent the firmware update from launching in the first place. This is due to your DAW occupying the Bootloader MIDI connection, although this connection needs to be used exclusively by Lié in order to perform the update.
To solve this issue, please head to the MIDI section within the preferences of your DAW and deactivate the inputs & outputs named “TOUCHE_BOOTLOADER” or “TOUCHE_SE_BOOTLOADER”.
Touché stays in Standalone Mode and the connection indicator stays greyed out although the device is connected? If Lié and Touché (SE) permanently fail to recognize each other, it makes sense to start from scratch by deleting Touché (SE)'s driver entries from your computer altogether. Read this article to learn how it is done:
How can I reinstall the Touché (SE) driver if my unit is not recognized correctly?