The EOS Lens registration data is intended to be used by either:

• The camera when processing the raw data from the sensor to produce a jpeg image (or to produce a jpeg preview image when the file is being saved as raw data). At a minimum the camera uses the information to do Peripheral Illumination Correction. Some but not all Canon EOS cameras can also apply Chromatic Aberration and Distortion corrections in-camera.

OR

• Canon's Digital Photo Professional image editing application. With DPP the available corrections include those for chromatic aberration, color blur, peripheral illumination, and geometric distortion. Recent versions of DPP also include the Digital Lens Optimizer tool that is even more powerful. It can even reduce the effections of diffraction caused by an aperture narrower than the camera's Diffraction Limited aperture (DLA)! But the DLO tool requires more detailed lens profiles than the data contained in the smaller profiles obtained via the Lens Registration Tool.

(Some of the top Canon cameras can even do DLO in camera as well as with DPP after the fact.)

Applications such as Lightroom or Aperture use their own lens correction data. As you have discovered, the data from Canon's Lens Registration Tool is not in a form that can be accessed and used by those other applications.

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You can download an updated user manual for your EOS 7D Mark II that includes the major changes made with firmware revision 2. It is available from Canon's support site for the 7D. Be sure to download the file named eos7d-im5-en.zip released on 06/28/12 rather than the "recommended" eos7d-im2-en.pdf released on 02/12/10. The older file is for firmware version 1. You'll need to extract the pdf from the zip file on your local machine.

The single question you cited in dismissing Canon's Digital Photo Professional is a distorted and one-sided view of version 3 of DPP which was very limited compared to what is available today with DPP version 4. For the other side of the coin, please see this answer to Why pick DPP over Aperture?

For the most part, it seems to me that those most vocal about the shortcomings of DPP in various versions are those who are already very well familiar with other applications and then try DPP for a very short time before dismissing it. Like any full-featured and complex application it takes a while to learn the ins and outs and to even discover many of the features and the power of what they can do for the user.

It may well not be the best raw conversion software for you, but it may also offer far more than you think it does, especially the current version which was a major upgrade from version 3. I personally prefer it for the more precise control it gives over color compared to Adobe Lightroom. You always have the option to export images as 16-bit tiffs before working on them in other applications (which is pretty much the way Adobe Camera Raw does it from within Lr or PS before using many of the other tools available in PS). It's not required to reduce them to jpegs when exporting.

As to the particulars of lens correction with regard to EOS cameras, in camera correction, and DPP vs. other apps please see: Canon DSLR Lens Correction