CIELAB uses the same Y. Sure they apply a nonlinear function to it, but if all you do is convert to CIELAB, remove chroma, then convert to sRGB you'll get an id

CIELAB uses the same Y. Sure they apply a nonlinear function to it, but if all you do is convert to CIELAB, remove chroma, then convert to sRGB you'll get an identical result. The only real difference is what gamma function to use, but the one used here (or even just square/squareroot) should give results that are nigh impossible to tell apart from sRGB.