Bake lightray-direction into Lightmap? "Directional irradiance-maps", Cycles

Hi everyone!
I’m currently experimenting with Cycles for Lightmap-baking. My problem is that conventional lightmaps pretty much ignore the normal-maps of my surfaces.
I’m now trying to bake the direction the light hits the surface (relative to the surface normal) into the lightmap,
so I can later produce correct lighting for my normal-maps.

Any ideas on how to do this? I don’t have a lot of experience in Cycles, so I don’t know if it’s even possible…
Thanks in advance :slight_smile: