The CIELAB space in Adobe Photoshop is the same space as that used everywhere else including the GretagMacbeth conversion software. All I can imagine is that you are having issues with the encoding. In CIELAB, L* ranges from 0-100, but is encoded as 0-255 in Photoshop. Thus, the Photoshop L values need to be divided by 2.55 to get ordinary L* scaling. For the a* and b* dimensions, there is a simple offset. Photoshop values of 0 to 255 are equivalent to CIELAB a*b* values of -127 to +128. This allows the positive and negative values of CIELAB a* and b* to be represented as simple 8-bit (0-255) numbers in Photoshop. Thus Photoshop a*b* values need to have 127 subtracted from them to get ordinary a*b* scaling. Perhaps it is this conversion that you are missing. (Note that this conversion might only be approximately correct depending on the color management settings in your system, Photoshop, and your software versions, OS, etc.