[Honor 5X Questions & Answers] Et tu Brute?:
It worked! I finally got LineageOS working. Thanks to ShadySquirrel and PalakMi for your verification of my installation!

So here is my ultimate tutorial how to install LineageOS 14.1 (= Android 7.1.2) on a brand new Huawei Honor 5X KIW-L21 that comes originally with a Huawei branded Android 5.1.1:

Step 0: Preparation

You have up to date Google USB drivers installed

adb and fastboot are working

You know how to check checksums

You checked your device: It's a KIW-L21 with a Huawei version of Android installed, version 5.1.1 and EMUI 3.1. Your device is called "kiwi".

With your detailed device information, you ordered an unlocking password from Huawei (except your phone is already rooted)

Step 1: Install Stock MM (= Marshmallow = Android 6.0)

Root the phone via fastboot until the fastboot & rescue mode screen says "OEM Unlocked, FRP Unlocked"

You can reach the fastboot & rescue mode screen by plugging your phone via USB to a PC and keep volume-down + power buttons pushed until you see the Honor logo

Download the following images and its checksums and check them to avoid corrupted files:

- Stock recovery image from Extracted_L21_B130.zip: L21_B130\RECOVERY.img

- Stock MM from this nice file depot of the Honor 5X in this forum: KIW-L21 C432B350 - D003

Flash the stock recovery to the phone with fastboot when you are at the fastboot & rescue mode screen: "fastboot flash recovery RECOVERY.img"

Copy the UPDATE.APP of the above file to /dload/ at an external SD card and put it into the phone

Hold both volume buttons and the power button until reboot

The Honor reboots into an autorecovery mode, installing the file from UPDATE.APP automatically

Wait until it's ready and be happy about your Honor 5X with Stock MM

Check if you are at this status: Huawei Honor 5X with a Huawei-branded Android 6.0.1, EMUI 4.0, build KIW-L21C432B350, custom version CUSTC432D003, fastboot & rescue mode screen saying "PHONE Unlocked"

Step 2: Install LineageOS

Download the following images and its checksums and check them to avoid corrupted files:

- TWRP 3.1.1.0 recovery image for the Honor 5X (kiwi): twrp-3.1.1-0-kiwi.img

- LinageOS 14.1 nightly build for kiwi devices: lineage-14.1-20170816-nightly-kiwi-signed.zip

- Open GApps package for ARM64 / Android 7.1 (in my case I choose "pico" to have the calendar and Google Play): open_gapps-arm64-7.1-pico-20170819.zip

Place the files where you can reach them from your adb/fastboot-console

Connect phone via USB to PC

Keep volume-down + power buttons pressed until phone restarts and shows Honor logo, release buttons; "Fastboot & Rescue Mode" screen should appear

On PC, check with "fastboot devices" if phone is connected and ready to go (should list an ID and the state "fastboot")

Flash recovery with "fastboot flash recovery twrp-3.1.1-0-kiwi.img"; should report sending and writing with two "OKAY" messages and a "finished"

Try to start recovery mode by keeping volume-up + power buttons pressed until Honor logo appears, release buttons and wait ~ 20 seconds

In my case, this started the Huawei eRecovery – you don't want that (and it's not part of the LineageOS wiki)

Navigate with the volume buttons to "Reboot" and press the power button; phone should boot normally

Once your old Android is up again, activate USB-debugging

Check if adb is connected to your PC with "adb devices"; you must allow access to the device on your phone when prompted, the device should appear with the serial number and the state "device"

Restart into the recovery mode you really want with "adb reboot recovery" and wait until TWRP boots; allow writing on its first start

Check if adb is connected to your PC with "adb devices"; the device should appear with the serial number and the state "recovery"

Push LineageOS image and Google apps to phone with "adb push lineage-14.1-20170816-nightly-kiwi-signed.zip /sdcard/" and "adb push open_gapps-arm64-7.1-pico-20170819.zip /sdcard/"; both should report transferred size and time

Do not forget to push the md5 checksums if you are paranoid like me

Backup everything to an external SD card from the Backup menu in TWRP (needed 4021 MB of space and took ¼ hour in my case)

Seriously, backup! Even though you haven't done anything with the phone yet. You have a running firmware, that's worth a lot :)

In TWRP, select "Wipe" and then "Advanced Wipe"

Check "Cache", "Data" and "System" and swipe to wipe

Go "Back" to return to main menu, then select "Install"

As you have backed up to an external SD card, "Select Storage" to "Internal Storage"

Navigate to "/sdcard", select lineage-14.1-20170816-nightly-kiwi-signed.zip and swipe to confirm flash; should not take more than a minute

When it's done, do not reboot but navigate back to "Install" and install Google apps by selecting open_gapps-arm64-7.1-pico-20170819.zip and swiping to flash

Once installation has finished, return to the main menu, select "Reboot", and then "System"; the Honor logo will appear shortly

LineageOS 14.1 is now being initialized

Disconnect phone from PC

Profit!

I'll provide links to the images as soon as this forum allows me to.