Oh, that’s right, forgot…
So, in the ICC transform, there are two steps: camera → PCS, then PCS ->destination. If the camera profile converts to Lab, then the destination profile needs a matrix/LUT that converts from Lab. I don’t have any; I use Elle Stone’s ‘well-behaved’ profiles for most of my destinations, and those are all XYZ anchored.
Unless I’m missing something about the process, which is likely…