The first Import returns the correct space (Lab).
In[4]:= Import["Desktop/m9-lab-tests/lab-4pix-input.tif", "ColorSpace"]
Out[4]= "LAB"
The second returns the same (apparently) wrong values.
In[5]:= Import["Desktop/m9-lab-tests/lab-4pix-input.tif", "Data"]
Out[5]= {{{1., -0.500008, 0.496101}, {1., 0.496101, 0.496101}}, {{1., -0.500008, -0.500008}, {1., 0.496101, -0.500008}}}
So I guess I have to update to v11 ...
Thanks for your feedback !