"Here is an illustration showing the limits imposed by this integer encoding of Lab:"

3D view is nice.

I made a layered 2D .pdf view and posted to this group ... years ago.
check here:  https://groups.io/g/colortheory/files/2015%20and%20earlier/Doug.S%20LAB%20curves
And check out the Lab gamut diagram.pdf
Useful to check if a test sample (Lab #s) in Lab, is in gamut...look it up on the chart.
Also useful to note at various L levels, where the a and b values are limited/out of gamut.
If anyone wants individual layers, I can post them here too.

Open .pdf and, for example, you can see that at L=50, lower left teal colors (-a and -b) are limited, and upper greens/yellows/reds are limited to b<80

Doug Schafer