There are a couple of RGB color spaces out there - LStar-RGB.icc and ProStarRGB.icc- that use the L* tone response curve. What's the supposed advantage of using the L* TRC over using a gamma curve as the TRC?
The intention behind L* was to make for a device independent colour space with a more neutral or 'flat' representation than available with Adobe RGB or sRGB. This is done by replacing the gamma with a set of calculated luminance values for the grey axis.
The L* colour space is said to exhibit less compression or blocking in when you make changes such as applying an S-Curve to increase contrast.
Colour guru Dan Margulis seems keen on L* (certainly over Adobe RGB, sRGB and ProPhoto RGB) writing:-
I believe that everyone agrees that if we wanted something with a gamut that approximates that of sRGB, there would have been better choices than sRGB. And for sure, if we had wanted something to give us approximately what Adobe RGB does, then Adobe RGB is a poor choice. But in spite of the fact that these are clearly undesirable defaults, they have won out.