I have solved it, here is the solution on my X1 Carbon with Windows 8.1 Pre-installed:

In Windows:

• First, You need to Disable Fast Boot.
• Open Control Panel and Search for Power Button.
• You should see a few lists (they might not be expanded, so click the arrow on the right).
• Look at the Shutdown Settings area.
• You want to uncheck Turn on fast startup (recommended)
• To do that, the box is grayed out so at the top click `Change settings that are currently unavailable. Then do it.

In BIOS

• Disable Secure Boot
• Change your Boot Order so that USB HDD - This is EXTREMELY important otherwise Ubuntu will NOT install the boot record EFI mode, it will do Legacy.

Here we disable Secure Boot:

Next, Move the USB HDD to the TOP:

In Ubuntu

• To Get into Ubuntu the only way if it's installed or not (With a live-usb or live-cd) you MUST have your USB plugged in and your BIOS to check for a USB at the top of the list (I mentioned this in BIOS
• Now you must connect to the internet (Wifi for me, there are no ethernet ports on X1 Carbon).
• You can install Ubuntu from this point OR if it's already installed follow these instructions using Boot-Repair https://help.ubuntu.com/community/Boot-Repair -- This will fix it since you are in the non-legacy mode VIA this USB.

Your boot from Grub will look like this:

IMPORTANT: Do NOT Run EasyBCD and Deploy a new MBR, otherwise you have to REDO the Live-CD and Boot-Repair again. I do not mind GRUB 2 at all, I like it. However, if you choose to not listen -- Good luck! Let us know what you find!

Other

• BCD-Edit is nice to have, but I am not sure if using this caused problems or not since I already had Windows Installed.

I have solved it, here is the solution on my X1 Carbon with Windows 8.1 Pre-installed:

In Windows:

• First, You need to Disable Fast Boot.
• Open Control Panel and Search for Power Button.
• You should see a few lists (they might not be expanded, so click the arrow on the right).
• Look at the Shutdown Settings area.
• You want to uncheck Turn on fast startup (recommended)
• To do that, the box is grayed out so at the top click `Change settings that are currently unavailable. Then do it.

In BIOS

• Disable Secure Boot
• Make sure the Boot mode is UEFI (It's that by Default unless you changed it)
• Change your Boot Order so that USB HDD - This is EXTREMELY important otherwise Ubuntu will NOT install the boot record EFI mode, it will do Legacy.

Disable Secure Boot

You will probably get a "Non Secure" warning every boot, who cares.

Make Sure Boot UEFI is Set

Next, Move the USB HDD to the TOP:

In Ubuntu

• To Get into Ubuntu the only way if it's installed or not (With a live-usb or live-cd) you MUST have your USB plugged in and your BIOS to check for a USB at the top of the list (I mentioned this in BIOS
• Now you must connect to the internet (Wifi for me, there are no ethernet ports on X1 Carbon).
• You can install Ubuntu from this point OR if it's already installed follow these instructions using Boot-Repair https://help.ubuntu.com/community/Boot-Repair -- This will fix it since you are in the non-legacy mode VIA this USB. (Or I have simple instructions I used below)

Install & Run Boot-Repair

If you did NOT already install Ubuntu, you MIGHT not have to do this -- either way It's OK to do.

sudo apt-get update
sudo apt-get install -y boot-repair && boot-repair

I ran the Recommended

IMPORTANT -- The Boot-Repair MIGHT tell you to enter a few commands. I did them, It was about 4 or 5 lines total.

After it's complete, Reboot!

Your boot from Grub will look like this:

IMPORTANT: Do NOT Run EasyBCD and Deploy a new MBR, otherwise you have to REDO the Live-CD and Boot-Repair again. I do not mind GRUB 2 at all, I like it. However, if you choose to not listen -- Good luck! Let us know what you find!

Other

• BCD-Edit is nice to have, but I am not sure if using this caused problems or not since I already had Windows Installed and messed around with it too much. If you get GRUB loading you are DONE.