How do I compute the correlated color temperature of an Lab/Luv color coordinate?
You can’t compute correlated color temperature from CIELAB or CIELUV coordinates. Correlated color temperature is a metric associated with light sources and is computed from tristimulus values (XYZ) or chromaticity coordinates (xy, or u’v’). CIELAB and CIELUV are computed by normalizing out the light source so those coordinates no longer have the information you need to compute correlated color temperature.