Ah but the issue is, its based on the encoding color space, the values can change.
Yes, that is one of the main points in the article. The author suggests using L* to remove these ambiguities.
Also, there's been some debate about using a scale like this, instead of say how Lightroom presents the values using a scale of 0-100%. 50% gray is 50% gray, using a scale of zero to 255 is based on the encoding color space which can range from 1.0 to 2.2 (or further if for some reason, someone's using some exotic color space). Yes, a 50% gray in a 1.8 gamma space is different than 50% gray in a 2.2 gamma space but the nice thing is, its always presented to the user as 50%.
Your math is incorrect. Mid-gray (L* = 50) can be converted to gamma 1.8 or 2.2 values by use of Bruce Lindbloom's companding calculator. The normalized pixel values are 0.3907 for a gamma 1.8 space and 0.4635 for a gamma 2.2 space. The corresponding values in 8 bit are 99.62 and 118.2 respectively. Lightroom reports values in normalized notation for gamma 2.2.
If you create a mid-gray in Photoshop by filling an sRGB image with midgray (L* = 50), the sRGB pixel value in Photoshop is 119, close to the calculated value of 118.2. If you import this image into Lightroom, the pixel value is reported as 46.7 or 119 in 8 bit notation, not 50% as you claim.
If you read the paper, you will see documented inconsistencies between Photoshop and Lightroom.