[Solution]
Apparently, when you use AccuRig to create basic rig for your character the herarchy is following:
Head -> FacialBone-> Eyes. // And this is not supported by Look At in iClone - eyes should be directly underneath the Head bone.
So In order to fix this issue I had to delete all the bones below Base_Head and create new ones that are directly linked to head and are called EYE_L and EYE_R. (I used Blender for this step)
Additionally, i had to remove the old skin weights in CC before removing old bones and adding new ones (otherwise there would be a strange offset in CC when you would try to apply new skin weights.
What I'm trying to figure out now is why my brow/eye lids morphs are not affected by look at? Do you have any ideas how I can activate those? I use CC4 standard with FBX seq, which in CC4 looks good and I whenever i move the eyeball down the eye lid is affected. But not in iClone and LookAt? Any ideas?
Is there any documentation of how the bones and morphs should be structured for Look At to work properly?