This post on StackOverflow helped : Why I got wrong outputs for converting RGB to l*a*b* color values using MATLAB? - Stack Overflow
Basically (I'll have to research this further) but, using rgb2lab gives the expected numeric results :
Lab(:,:,1) =
53.5850 53.2408 97.1393
87.7347 91.1132 77.9855
96.5375 60.3242 32.2970
89.2650 68.0698 14.7631
Lab(:,:,2) =
0 80.0925 -21.5537
-86.1827 -48.0875 16.7037
0 98.2343 79.1875
-12.5051 -66.1018 48.1573
Lab(:,:,3) =
0 67.2032 94.4780
83.1793 -14.1312 16.5673
0 -60.8249 -107.8602
43.9621 51.3645 -61.6661
Big sigh of relief!