[G Pad 10.1 General] fatbas202:
EDIT: If you are coming here for the first time, this guide should still work, but [MENTION=7559542]PorygonZRocks[/MENTION] has created a flashable zip that should deal with a lot of these issues automatically. You can check out his post here:

https://xdaforums.com/showpost.php?p=75787067&postcount=699

This method will indirectly allow you to root the LG Gpad v410 after it has been upgraded to Lollipop 5.1.1. Yes. Rooting LG v410 Lollipop. It's through a downgrade, but it works.

It took a while to get working, but here's how I did it. The process is straightforward, but the details matter greatly. You will brick your device if you mess up. Please read everything *first* before you do anything. Be sure you understand the process. I'll try to explain what's going on along the way.

An external SD card is extremely helpful for this process. You *could* adb push everything, but that will tedious.

First, you need some files.

The 4.4.2 KDZ which is a TEST OS, but it can be rooted and it downgrades to a Bump'able bootlaoder:

http://xdaforums.com/g-pad-10/general/kdz-lg-g-pad-7-0-v410-t3224867

The LG 2014 Flash Tool:

http://www.mediafire.com/download/fwrcd3pdj0svjtb/LG_Flash_Tool_2014.zip

Android LG Drivers:

https://www.androidfilehost.com/?fid=24052804347802528

Parted for Android. You can probably find it other places, but I found this file:https://dl.dropboxusercontent.com/u/84115590/LG%20G2%2016GB%20Solution/sdparted-recovery-all-files.zip

EDIT: There seems to be a lot of confusion here. My bad. All you need is the file named "parted" from this zip file - nothing else. Just put that one file in the root of your external SD card.

https://dl.dropboxusercontent.com/u/84115590/LG G2 16GB Solution/sdparted-recovery-all-files.zip linked from here: http://www.**********.com/your-32gb-lg-g2-shows-only-16gb-storage-space-heres-the-fix/

EDIT2: The dropbox link is down. I've attached the file directly.

The Candy5 ROM (This will potentially save you some manual steps. Somewhat optional, but highly recommended):

http://xdaforums.com/g-pad-10/development/rom-candy5-g-pad-v410-lollipop-5-1-1-v2-t3111987

Flashify APK:

http://www.apkmirror.com/apk/christian-gollner/flashify/flashify-1-9-1-android-apk-download/

TWRP for the v410:

http://xdaforums.com/g-pad-10/development/recovery-twrp2-8-5-0lgv400-410-t3049568

LG One Click Root:

http://xdaforums.com/lg-g3/general/guide-root-lg-firmwares-kitkat-lollipop-t3056951

(You may use Purple Drake or whatever else you want. They all use the same root script as this does and the GUI is helpful for novices.)

Android SDK (specifically adb.exe. After installing go to SDK Manager and ensure that Android SDK Platform Tools is checked):

http://developer.android.com/sdk/index.html

For clarification below, when I have commands in "quotes" they are Windows commands. When they are in `backticks` they are commands that you run inside of ADB which actually run on your device....as root. Root can screw things up. Please be extra cautious. If you blame me for messing up your device I will laugh at you. But that's not gonna happen, right? Good. Let's go.

Now that you have everything, put it all into a folder where you can access it easily.

Install the LG Drivers.

Install Android SDK (or otherwise get adb.exe).

Extract all of the archives.

Move the KDZ to the LG Flash Tool 2014 folder.

Put the tablet into Download Mode by powering it off, holding VolUp, and plugging in the USB cable. Press VolUP when instructed. You must be in Download mode before continuing.

Run LGFlashTool2014.exe. Select the KDZ file. Click "CSE Flash". Click "Start". Select "English" and click OK. Do not change anything else.

WAIT for the flash to continue. If you really want to brick your device, here's a good opportunity.

The device will reboot into Android 4.4.2. You will only have 4GB of internal storage at this point. DON'T PANIC! We are fixing it.

Enable USB debugging.

Connect the device.

Install and run LG One Click Root. Wait for the device to be rooted before proceeding.

Copy the Flashify apk, TWRP image, and Candy5 ROM to your external SD card.

Install Flashify and flash TWRP to the recovery partition.

Use the Flashify menu to reboot in to recovery.

DON'T PANIC! You will get white vertical lines on the boot screen from now on. They only show up during boot animations. A small price to pay. This may be fixed at a later date. for the time being! Thanks to marcsoup's first post ever, we have a fix! Details below. PLEASE click this link and thank him!

Things get tricky here. Copy parted to your external SD card and then run "adb shell" from Windows to get a shell in TWRP.

In TWRP, unmount /data by tapping Mount > uncheck Data.

`cp /sdcard/parted /sbin/` This copies the parted binary to /sbin so it can be executed in the path. I had trouble running `/sdcard/parted`, but YMMV.

`chmod +x /sbin/parted` Make it executable.

`parted /dev/block/mmcblk0` Run parted against the internal mmc

`p` Prints the partition table.

`rm 34` Deletes partition 34 labeled "grow". This is the root of our problem. The KDZ apparently only creates a 4GB partition, I assume so the test build has maximum compatibility with all sized devices.

`rm 33` Deletes partition 33 "userdata"

`p` Print to verify

`mkpartfs` Create a partition and put a filesystem on it. If we only expand the partition it won't help us because the filesystem is still only 4 GB.

a) name: userdata

b) type: ext2 (the tool only supports ext2. This is ok for now.)

c) start: 3439MB (the end of part 32. IT MAY BE DIFFERENT FOR YOU!) Be sure you do not omit the MB part otherwise the offset will overwrite another critical partition.

d) end: 15.8GB (where "grow" ended above. IT MAY BE DIFFERENT FOR YOU!) Be sure you do not omit the GB part otherwise the offset will overwrite another critical partition.

`p` Verify. For me it did not name the partition properly. Gotta fix that.

(if necessary) `name 33 userdata` This is critical for mount to find it in /dev/block/platform/msm.sdcc.1/by-name/ on some/all ROMS.

`p`. Verify one last time. Compare it to my partition table in the attachments. If you want to brick, delete some random partitions here.

Flash Candy5 with TWRP. It's only 239 MB, so it will flash quickly. I do this because Candy5 will reformat mmcblk0p33 from ext2 to ext4 for you. It does this as part of it's system boot, apparently. If you install a different ROM that does not do this, you can reformat it by running `make_ext4fs /dev/block/mmcblk0p33`. If your ROM does not have make_ext4, it likely has some differnt method to make an EXT4 filesystem. `/system/bin/mke2fs -t ext4 /dev/block/mmcblk0p33` may work better. Just flash Candy5 and be done with it.

Tap Wipe > Swipe to Factory Reset.

Tap Reboot > System.

WAIT!!! It will take a minute for the ROM to start the first time. You will have white lines and and possibly a white screen. WAIT. It's moving the DEX files to cache, formatting a partition, creating default folders on the internal storage, and several other things. WAIT! When the screen goes dim or turns off then it's ready.

Cycle the display or turn it on. You should be at the Candy5 lock screen.

USB debugging is on by default. Run "adb shell".

`mount | grep userdata` Make sure mmcblk0p33 is mounted.

`df` Make sure /data is 11.3 GB (or whatever size it is on non-16GB devices).

HELL YEAH, you downgraded, rooted, and fixed the partition problem. Enjoy your tablet!

Thanks to dopekid313 for finding the KDZ.

Thanks to timmytim for Candy5.

Thanks to the creators of the root script, flashify, TWRP, and XDA for being so awesome.

Thanks to marcsoup for fixing a fix to the white lines.

Thanks to navin56 for the partition dumps. PLEASE thank his post!

White lines fix.

What we are going to do is flash the aboot partition with the stock image provided by navin56. I've removed the extra files from the dump, so simply download aboot.img.7z below. Unzip it using 7zip.

These commands are to be run in TWRP. Reboot to TWRP recovery and connect with "adb shell". All of the following commands will be run in ADB under TWRP. If you cannot figure out how to get here, please post in the thread and someone will help you. Onward:

If you do everything correctly then you don't have to reflash your ROM and you won't lose data. This process can be done any time after flashing the KDZ, even before you follow the steps above to resize the userdata partition. It's a completely separate process.

Unzip aboot.img.7z so you have the file named aboot.img. You should also make sure that aboot.img's MD5 sum is e97431a14d1cee3e9edba513be8e2b52. Do not flash the 7z file. Please.

Copy aboot.img to your external SD card. It should live at /sdcard/aboot.img

Boot to TWRP and run "adb shell"

`ls -al /dev/block/platform/msm_sdcc.1/by-name/` Let's make sure we are flashing the right partition. On my device "aboot" is /dev/block/mmcblk0p6. You should verify this on your device or you WILL brick your tablet.

`dd if=/dev/block/mmcblk0p6 of=/sdcard/aboot-fukt.img` Let's back up our current aboot partition before we go flashing things just in case there are unintended consequences later. Be sure you have the same partition that "aboot" referred to in the 4th step or you have just backed up the wrong partition.

`dd if=/sdcard/aboot.img of=/dev/block/mmcblk0p6` Be sure the file exists, is the correct aboot.img, and you are flashing the right partition. You have been warned!!

Reboot TWRP and enjoy your boot animations again.

If I missed anything, please let me know. As far as I know this is the very first tutorial that details what is necessary to accomplish this. Please hit the Thanks button on every thread that you visit to download files!

FAQ:

Q: Why do I only have 11.3 GB of space when my device is 16GB?

A: The entire internal SD card (eMMC) is 16 GB. Gotta have someplace to install the bootloader, recovery, android, the modem OS, the secondary bootloader, the cache, the resource and power manager, and all of the other partitions necessary for the table to operate. Please look at the second screenshot in the OP. All of those 33 partitions take up room on the internal card. Fortunately ALL of those partitions ONLY take up about 4.4 GB. Hence the 'userdata' partition is ~11.3 GB.