How does Photoshop calculate Lab values?

It might help to understand the quote below from the book “Real World Photoshop CS3” which was published in 2008. It also appeared in the book’s earlier editions by the late Bruce Fraser, as well as his book “Real World Color Management” published in 2003. Bruce didn’t just say that out of thin air. He worked closely with the Photoshop team.

The second quote, below, is from page 33 of “The Digital Print” (2014) by Jeff Schewe, who also works closely with the Photoshop, Camera Raw, and Lightroom teams.

Anyone who studies how Photoshop color works eventually understands that: 

• Lab is its reference color space for color conversions.
• Any color conversions must be corrected for the specific color space of the current color mode (such as sRGB vs Adobe RGB, or FOGRA CMYK vs US SWOP CMYK). 

If you show an Excel spreadsheet or color conversion table that doesn’t account for color space, or doesn’t use Lab as a reference color space, that conversion table is not useful or reliable when discussing Photoshop.

Colour management.

Make 2 separate RGB files, one sRGB, the other ProPhoto RGB. Type in the same set of RGB values and compare the Lab readings. Type in the same Lab values and compare the RGB readings.

It's the other way round. All color space numbers are calculated from Lab.

Lab is the reference and at the base of all color management. It is one of two commonly used Profile Connection Spaces (the other is CIE XYZ).

A standard profile conversion goes, say, Adobe RGB > Lab > sRGB.

Lab numbers define a color absolutely.