You are seeing the effect of different gamma encoding. Adobe RGB is 2.2, ProPhoto RGB is 1.8.
An example, RGB(128,128,128) has an L* value of 54.0 in Adobe RGB while it has 60.7 (significantly lighter) in ProPhoto RGB. This difference increases as the values get darker. With RGB values of (30,30,30) the differences expands and is quite noticeable at L* = 8 and 16.
When you convert from one matrix based colorspace to another, the values are changed such that the Lab values remain unchanged for all values within the gamut of the destination space. Neutrals are always in gamut between matrix spaces hence not changed upon conversion.
This is all purely a result of gamma differences. Note that sRGB is often stated, incorrectly, to have a gamma of 2.2. sRGB doesn't have a pure gamma, but a combination of a short, gamma=1 segment tacked in front of a gamma=2.4 segment.