There are various reasons why you don't see a LAB mode in Lightroom Classic. One is that LAB is not considered a mode that most photographers will need, so it’s missing for the same reasons that CMYK and indexed-color modes are not supported for editing.
I am one of those who got into LAB mode editing in the early 2000s, when it did provide some advantages over the RGB-based ways that most photo applications worked at the time. If you look at the citation at the bottom of the article you linked to, the article’s techniques are based on those of color expert (some might say genius) Dan Margulis, in a book he published in 2006. Those techniques were revolutionary then, but…
…that was a time when things were about to change quickly. Lightroom Classic originally came out in 2007. It was part of a wave of new-generation photo editors like Apple Aperture. In addition to being raw-first editors, they tried to be more photographer-focused than Photoshop. The controls were designed to be smarter about image quality, so that photographers could avoid some of the workarounds or tricks they had to do in Photoshop (like LAB conversion) to get better quality.
For example, one of the stated reasons to use LAB was to sharpen luminosity separate from color. The traditional Unsharp Mask in Photoshop did not natively do this, so you got color fringing. One solution was to convert to LAB mode and sharpen just the L channel. But after 2006, more photo editors starting building this in; Lightroom provides separate sharpening controls for luminosity and color without having to change the color mode. When Photoshop introduced Smart Sharpen they had it concentrate sharpening on luminosity, similarly negating an advantage of LAB.
The color targeting done in LAB can (mostly) be done in Lightroom using the HSL controls or Range Mask. For many photographers, these are much more intuitive than figuring out where to place curve points in LAB, and then, which way to drag them. This is another reason LAB is not in Lightroom; LAB can be hard to use. LAB curves are so counter-intuitive that someone highly experienced in RGB or CMYK curve editing can't apply their experience to LAB curves, because the way you place and move the points is completely different.
Regarding the fact that a lot of LAB color is not reproducible: People use LAB anyway, knowing that you have to keep your A and B curve moves away from the non-reproducible extremes. But that means you can really only work in the remaining center range of that little graph. In RGB and CMYK curves, it’s realistic to use the entire graph, but because you can’t use the whole A and B curves in LAB, the remaining range has coarser increments. You have to be more careful because small moves result in larger color changes compared to RGB and CMYK. It’s easy to go too far into unrealistic color, and I see that when I look at my old LAB-edited images.
I don’t think Lightroom has an equivalent for everything that can be done in LAB mode, and LAB editing is a good Photoshop skill to have when an image really needs it. But with today’s advanced tools in Lightroom, Photoshop, and other current photo software, it’s been a long time since I decided it was worth editing an image in LAB.
I think what your asking about is used by the program internally but expressed as RGB values because the original thinking behind LR was that the user wouldnt want to jump back and forth from one color space to another.
I think that is true of both Lightroom and Photoshop: We edit using RGB controls, but behind the scenes, color calculations are done in LAB. One reason is that LAB is flexible enough to preserve color quality during conversions between various color spaces and modes, such as converting from an RGB image to a CMYK 8-ink inkjet printer profile.
