OK, I have wrote a flashing guide for Windows users, tho I don't use Windows so I hope all steps are correct:
Flashing LOS on Cupid
Xiaomi 12 LOS ROM flashing
Your bootloader must be unlocked.
You should use latest platform tools on Windows. https://dl.google.com/android/repository/platform-tools-latest-windows.zip
Your device should be charged above 50%. Well, it doesn't have to be, but this is just for your phones safety.
Download all required files - ROM, boot, vendor_boot, dtbo and recovery.
Make a proper backup if needed and push it to another storage.
After you have unlocked the bootloader, device will reboot automatically. Finish the setup, enable developer settings and finally enable USB-Debugging in developer settings.
In Windows open the folder in which you have unzipped the platform tools.
Hold left shift and press right click
click "open powershell window here"
Type in Terminal for example "adb devices" and grant the permissions for this PC on your device.
Reboot your device to fastboot and connect it with your PC.
The flashing procedure:
Flash boot, vendor_boot, dtbo and recovery:
Type in Windows Terminal:
fastboot flash boot lineage-19.1-20220617-UNOFFICIAL-cupid-boot.img
fastboot flash vendor_boot lineage-19.1-20220617-UNOFFICIAL-cupid-vendor_boot.img
fastboot flash dtbo_ab lineage-19.1-20220617-UNOFFICIAL-cupid-dtbo.img
fastboot flash recovery lineage-19.1-20220617-UNOFFICIAL-cupid-recovery.img
fastboot reboot recovery or
reboot to recovery by holding volume up and power buttons until you see Mi logo on your screen (on device).
In LOS recovery:
do a factory reset first
go to "Factory reset" and perform "Format data / Factory reset"
all data will be erased. Then....
go to "Apply update", followed by "Apply from ADB"
Now sideload the ROM:
type in Windows Terminal
adb sideload lineage-19.1-20220617-UNOFFICIAL-cupid.zip
You can also drag ROM zip file into your terminal window, instead of typing the full name/path to file.
When finished, reboot simply your device.