It should be noted that for a touchscreen system, it is not Raspberry Pi OS lite that needs to be installed, but rather the full version.
In addition, before little-backup-box is installed, any display drivers that may be required should be installed so that the screen already works before little-backup-box is installed.
The rest of the installation is the same as the headless installation:

Follow the instructions at https://github.com/outdoorbits/little-backup-box and the wiki page Installation.

After installation, the Raspberry Pi will reboot and the user interface should appear on the display.

Little Backup Box in a touchscreen housing - watch Dave's video on YouTube