The best axis for Lightness in my opinion is still the Gray-Scale (as used back in the day for black/white/grayscale TVs).
The newer CIE colorspaces (CIECAM02 CIECAM16) seem to address the effect, that color-perception goes wild if you change background and illumination. Oklab seems to only make some fixed choice about how to include the chromatic part to lightness. I'm not so sure, how this definition of lightness is any better than grayscale (from 1931).