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I tested your Lab color L 37.6, a 3.6, b 6.1, using CS3 InDesign and Photoshop. Photoshop rounds the numbers. When I input Lab values L38, a 4, b 6 into both apps, using Absolute rendering and FOGRA39, I get the same CMYK data: C49, M49, Y 54, K 44.
More than likely InDesign is hosing the CMYK result. Do not change the swatch to CMYK. Leave it as Lab, set to Process. Use Window: Output: Separations Preview. Put your cursor over an object using the swatch color and observe the CMYK readouts.
Regarding the GCR - no, there is no way to use Photoshop or InDesign to change GCR parameters for FOGRA39. You need separate profile editing software for that task.
Hope this helps.
OK, I found the problem.
In Photoshop I have to create a new SoloidColour object between conversions to get ride of old values.
Thanks a lott