In this paper, the effect of labeling for higher dimensional lattice quantization index modulation techniques is studied. The studied problem is similar to Gray Codes in 1 dimension but critically differs as the cosets are not linearly arranged but spread in different directions. A thorough analysis will show the impact of this problem on the overall performance of the studied systems. We present heuristic solutions for specific systems and determine a lower bound on the impact of incorrect labeling. Our analysis will include (1) robustness against JPEG and JPEG2000 compression and (2) transmission over an AWGN channel.