If I were to convert RGB into Lab in Photoshop I’d get a cmyk value where k is non zero, and the values of c,m and y similarly so but dependant upon the maximum inl levels. So I assume that there is not one fized and definitive transformation, it depends on the profile used to define the cmyk working space.
To underscore the point, I could simplistically add the k values back into the c, m, and y and use a k value of Zero … unfortunately I’d likely end up with values in cmy of greater than 100 …which I’d not be able to use.
Further, if I make a new custom cmyk profile with photoshop where I select no K and a maximum of 300 ink, I obtain another set of coordinates again … but the sweet thing is that the image looks just the same.
What this says to me is that, if I can get 3 different sets of cmyk values for a single set of RGB, then there is no unique and universal Lab profile … all would be vendor specific.
Now photoshop have one called Lab Color that you could use in converting to cmyk but would that be the same profile that you are using in your conversion from RGB?
That is the rub.