[Galaxy Note 10.1 General] carlosmessala:
First of all, I'm not the responsable for none of this great development work and I'll try to link every step to the source where I found each one and credit it to the right person.

I thought was important to post it here because, thanks to the Samsung, the Galaxy Note 10.1 have too many different device specs under the same product name and the internet is crowded with wrong tutorials or misleads.

If I said something wrong in this post, feel free to correct me or delete it if necessary.

The user Skyjumper at android-hilfe.de forum shared his experience testing an unofficial version of LineageOS 14.1 for GT-N8000 (2012) in GT-N8020 (2013). He also linked two XDA permalinks for comments with links to [1] TWRP 3.0.2 (by Aramir_, at here) and [2] LineageOS 14.1 unofficial (by lirokoa, at here). Then you have just to download the openGAPPS (I would suggest pico version), the Odin3 and the LineageOS add-on for SU (optional for who want SU access).

DOWNLOAD FILES

I uploaded every file for this tutorial to Google Drive because most of the websites have low speed traffic control, but feel free to download from where you want.

Odin3 v3.13.1 [xda] [gdrive]

Samsung Stock Rom [gdrive]

TWRP 3.0.2 [xda] [gdrive]

LineageOS 14.1 Unofficial [xda] [gdrive] - copy this file to your SDcard to be accessed by TWRP

LineageOS Add-on for Super User [lineageos] [gdrive] - copy this file to your SDcard to be accessed by TWRP

GAPPS [open GAPPS] [gdrive - pico] - copy this file to your SDcard to be accessed by TWRP

STEP 0 - go back to stock ROM throught Odin (just to be sure) *OPTIONAL

Activate the Developer Mode by tapping seven times the VERSION NUMBER ate ABOUT TABLET menu;

Activate the USB Debug at the development menu;

Restart the tablet in Download Mode (power button + volume down);

Open Odin and plug usb from tablet to computer, then select the stock ROM file (you have to extract the RAR file and use the *.tar.md5 file) and click start.

STEP 1 - install the custom recovery TWRP 3.0.2 throught Odin

Activate the Developer Mode by tapping seven times the VERSION NUMBER ate ABOUT TABLET menu;

Activate the USB Debug at the development menu;

Restart the tablet in Download Mode (power button + volume down);

Open Odin and plug usb from tablet to computer, then select the TWRP tar file and click start; at this point, the device will reboot and you have to be fast and hold power button + volume up to boot in recovery mode (if the system reboot, it will replace the custom recovery back to the default one and you will have to install the TWRP again with Odin.

STEP 2 - install the LineageOS and others tools throught the new TWRP - (only reboot at the end of the entire step)

In the TWRP, click WIPE, then ADVANCED WIPE and select CACHE and SYSTEM and wipe it, then click to FORMAT DATA to format it too;

Back to main screen, click INSTALL, select the SDcard storage and navigates until the LineageOS 14.1 zip file and swipe to instal;

Go back and click INSTALL again, and select the Google Apps file and swipe to install;

*OPTIONAL - Go again to INSTALL and select the the LineageOS add-on for Super User;

Reboot the system and do the initial configuration.

Know issues

The default device name at bluetooth configuration becomes GT-N8000, and you may want to change it back to GT-N8020 or any other you want;

The virtual keyboard starts hidden by default, then, at the initial configuration, when you will type your wifi password, you will have to activate the virtual keyboard visibility in the right bottom corner;

The configuration or MPT apps may stop working at the boot time, but just click the option to close and it will restart;

All the build mention at /system/build.prop is now N8000. I tried to edit the file to fit the real spes, but, to be honest, I don't really know what this really means, but still works properly to me.

Unknow issues

I couldn't test the SIM card usages and bluetooth yet. I'll try to edit this post when possible.

Additional steps

To activate the Super User, activate the Developer Mode (same as steps 0 or 1) then activate it at the Development menu;

The pico version of Google Apps installs only the necessary to run the Google Play app, now you may want to install the rest of essential google apps that you use.