Transforming RGB images including NIR to LAB
Let's start with the source of your RGB + near IR images. To break the process down:


Some camera must have taken those images.
The camera sensor is sensitive to light within two given wavelengths. The technical term for this is spectral response.
Alternating elements (Bayer pattern) in a sensor are etched with filters. Each filter type passes certain wavelengths while supressess the others.
The alternating sensor elements accumulate the filtered light from different wavelengths. This creates our very first raw signal. This raw space is then mapped onto a color space, most commonly the sRGB space.
Filter properties are precisely measured by the manufacturers. They use those properties (and assume a D65 white point, unless manually chosen to something else) to convert the captured raw space into sRGB which gets passed down to you (usually with a little compression and anti-aliasing filtering).


Answering your final question first, with the sRGB assumption in place, you are now armed with one very important source of information - your white point is D65 unless explicitly stated elsewhere. You may now safely proceed to convert your sRGB image into LAB. MATLAB has a handy function for the same.

To answer your questions:


  First question would be: is that correct, or did I just fall for
  single people claiming something?


A: People say a lot of things - largely from their personal experience. You must create your own. I personally exect LAB to help. You can read more about that on my Quora answer here. 


  Is there a way to properly include NIR in the LAB color space? Or
  would it be better to keep it as separate information?


All traditional color spaces are designed to fall within the locus of human perception. Since near IR is out of bounds for our perception, it's usually modelled as a standalone entity (seperate channel). However, many imaging devices have a near IR spectral response below 750 nm. If that's the case, I would expect statistical correlation between your G or R channels with near IR. A simple PCA would answer that question.