Take an Adobe RGB JPG, convert it to Lab, then save as a JPF or PDF (probably any format). You'll note this metadata:
xmp:xmp-photoshop:colormode:Lab
xmp:xmp-photoshop:iccprofilename:Adobe RGB (1998)
No bueno. My guess is that the field is just not being blanked or populated upon conversion to Lab.
Sending love and best wishes to all readers! Peace.